Student Papers
Complex Adaptive Systems
Fall 2012
Edited by
Ivan Garibay
CS-TR-12-05
Complex Adaptive System Laboratory
University of Central Florida, January, 2013
Preface
3
Papers
A New Fast Agent Based Adaptive Algorithm
to Estimate Real Time Phasors
Syed Alam Abbas
4
An Agent-Based Model of Ant Colony
Conflict
Charles Snyder
12
Effects of Wealth Distribution In a
Progressive Tax Model
David Gross
21
A New Measurement of Complexity for
Cellular Automata: Entropy of Rules
Fan Wu
31
ASOP- Adaptive Self-Organizing Protocol
John Edison
39
Agent Based Model for Leftover Ladies in
Urban China
Jun Ding
47
Wealth Redistribution in Sugarscape:
Taxation vs Generosity
Vera Kazakova and Justin Pugh
58
Cooperative Coevolution of a Heterogeneous
Population of Redditors
Lisa Soros
73
An implementation of CHALMS (Coupled
Housing and Land Market Simulator)
Michael Gabilondo
78
Power Vacuum after Disasters: Cooperating
Miguel A. Becerra
85
1
Gangs and their effect on Social Recovery
Multi-agent based modeling of Selflessness
surviving sense
Taranjeet Singh Bhatia
93
The Effect of the Movement of Information
on Civil Disobedience
Yazen Ghannam
98
The Effects of Hygiene Compliance and Patient
Network Allocation on Transmission of Hospital
Acquired Infections
Zachary Chenaille
106
2
Preface
These proceedings contain the student papers presented as final projects for the
Complex Adaptive Systems class (CAP 6675) that I taught at the University of
Central Florida the Fall of 2012. All papers in this collection present original
research in the area of Complex Adaptive Systems developed during the course of
this class.
More information about this class can be found at
http://ivan.research.ucf.edu/teaching.html
Ivan Garibay
Orlando, January 2013
3
1
A New Fast Agent Based Adaptive Algorithm to
Estimate Real Time Phasors
Syed Alam Abbas, Student Member, IEEE, and Ivan Garibay, Senior Member, IEEE
and phasor estimations over a wide range with fast response.
Although better performance can be achieved by these optimization techniques, the implementation algorithm is more
complex and intense in computations.
Window based methods such as discrete Fourier transform
(DFT), short time Fourier transform (STFT) and wavelets are
also applied extensively for real time estimation of power
system amplitude and phase parameters. DFT is desirable due
to its low computational requirement and fast response. However, the implicit data window in the DFT approach requires
a full cycle [5]. To improve the performance of DFT-based
approaches, some enhancements have been proposed. But due
to the inherent limitations in such methods, at least one cycle
of the analyzed signal is still required, which hardly meets
the demand of high-speed response especially for protection
schemes. STFT-based approach has limitations in its accuracy
and still requires half a cycle to respond. Recursive wavelet
transform (RWT) which is faster, can output phasor parameters
in a quarter cycle, has been proposed recently [6]. In this
method inappropriately selecting window length and sampling
rate may cause the weighting matrix to go singular. Also,
it has the inherent limitation of having more computational
requirements and higher sampling rate to achieve a reasonable
accuracy in short time. A combination of algorithms has also
been used to overcome individual limitations [7].
In this paper the estimation is done using a combination
of agent based modeling and linear adaptive filtering techniques. The phasor quantities to be determined are modeled
as weights of the linear filter that acts an independent agent.
This way the model can be easily adapted to drifts in the
nominal frequency for each component separately, when it is
known, easily tracking its amplitude and phase changes. Each
agent uses adaptive block least mean square algorithm (BLMS) with optimally derived step sizes and conjugate gradient
search directions , rather than gradient based directions, for
minimizing the mean square error (MSE) or the cost function
of the linear system. In simulations the performance of this
new algorithm is compared with number of other popular
published algorithms, both model based and window based.
The paper is organized as follows: Section II describes
the formulation of phasor estimation as a linear filtering
problem Section III shows the formulation using agent based
model. Section IV gives the overview of the conjugate gradient
technique and B-LMS algorithm and the proposed method
used for each agent. In section V the simulations results are
presented in comparison with the other algorithms followed
by conclusions in Section VI.
Abstract—Phasor magnitude and angle of various harmonic
and interharmonic components of the power signal are widely
used as critical variables and performance indices for power
system applications such as protection, relaying and state monitoring. This paper proposes a novel adaptive agent based algorithm for estimating the phasor parameters in real time.It uses
decentralized and parellel agents trying to compete and cooperate
for accurate and speedy estimation of phasor parameters. Each
agent has a designated nominal frequency and it estimates and
tracks drifts in amplitude and phase of the component using
linear filtering techniques. Each agent uses faster quasi-second
order optimization technique to estimate amplitude and phase of
single frequency component. This computation does not require
any matrix inversions. It features fast response, achieves high
accuracy and involves lesser computational complexity than many
other model and window based methods.
Index Terms—Agent based modeling, Phasor amplitude value,
phasor angle, harmonic and interharmonic component estimation, phasor estimation, adaptive signal processing, Block LMS,
conjugate gradient based search
I. I NTRODUCTION
P
OWER systems in many applications require real-time
measurements of phasor magnitude and angle of the fundamental component and the harmonics present in the voltage
and current signals of the power line. These are parameters
of critical importance for the purpose of monitoring, control
and protection. Speedy and accurate estimations are required
for a proactive response under abnormal conditions and to
effectively monitor and preempt any escalation of system
issues.
A variety of techniques for real-time estimation of phasors
has been developed and evaluated in past two decades. They
are either model based, least error squared (LES), recursive
least square (RLS) [1], Kalman filtering [2] or other window
based methods. They all use the stationary signal sinusoidal
model. LES, RLS, Kalman filters are more suitable for online
processing since they generate time trajectories of the evolved
parameter but the complexity involved is significant and the
matrix has to be fixed and accurate for the model to work.
Any drift from the assumed nominal frequency will render
the model highly inaccurate. Some artificial intelligence techniques, such as genetic algorithms [3] and neural networks
[4], have been used to achieve precise frequency estimation
S. Alam is with the Department of Electrical and Computer Engineering,
University of Central Florida, Orlando, FL, 32816 USA e-mail: (syedalamabbas@knights.ucf.edu).
I. Garibay is a joint faculty with the Department of Electrical and Computer
Engineering, University of Central Florida, Orlando, FL, 32816 USA e-mail:
(igaribay@ucf.edu ).
Manuscript submitted November 27, 2012.
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II. MODELING PHASOR ESTIMATION AS A
LINEAR FILTERING PROBLEM
with the following equations:
p
Vp0 = w1 (n)2 + w2 (n)2
w2 (n)
θ0 = arctan
w1 (n)
p
Vph = w3 (n)2 + w4 (n)2
w4 (n)
θh = arctan
w3 (n)
Linear Filter: Consider a system with L inputs coming from
sensors placed systematically in the environment that does
weighted linear combination of inputs. Then the output of the
system is given by:
y(n) = x1 (n)w1 (n) + x2 (n)w2 (n) + ... + xL (n)wL (n) (1)
Such a system is called linear filter and the weights can be
adaptively estimated with some algorithm.
Clearly, if the harmonic or the interharmonic we seek is
absent in the signal, the corresponding weights describing it
in the linear system will be close to zero.
A. Phasor estimation model with fundamental and harmonics
Let us consider a discrete input signal that contains fundamental frequency with the sampling period ∆T . Also without
loss of generality we will consider a harmonic h of the
fundamental frequency in the signal; where h need not be
an integer.
B. Phasor estimation model with decaying DC component
Let us consider a discrete input signal that contains only
fundamental frequency with the sampling period ∆T and a
single decaying DC component.
y(n) = Vp0 sin[2πf0 n∆T + θ0 ]
+Vph sin[2πfh n∆T + θh ]
n = 0, 1, 2, 3 · · ·
y(n) = Vp0 sin[2πf0 n∆T + θ0 ] + Vdc e
−n∆T
τ
n = 0, 1, 2, 3 · · ·
(2)
(4)
where Vp0 , f0 , θ0 represents the amplitude, frequency and
phase of the fundamental component and Vdc , τ are the
amplitude and time constant of the decaying dc component
present in the composite signal.
Then using Taylor’s series expansion upto first order for the
second quantity in (4), we have,
where Vp0 , f0 , θ0 represents the amplitude, frequency and
phase of the fundamental component and Vph , fh , θh the amplitude, freqency and phase of hth harmonic or interharmonic
if h is a real number such that fh = hf0 , in the composite
signal respectively.
Then using the trigonometric expansion,
y(n) = Vp0 sin[2πf0 n∆T ]cos[θ0 ]
+Vp0 cos[2πf0 n∆T ]sin[θ0 ]
Vdc · n∆T
+Vdc −
τ
y(n) = Vp0 sin[2πf0 n∆T ]cos[θ0 ]
+Vp0 cos[2πf0 n∆T ]sin[θ0 ]
+Vph sin[2πfh n∆T ]cos[θh ]
+Vph cos[2πfh n∆T ]sin[θh]
(5)
We use the following notations at this point,
We use the following notations at this point,
w1 (n) = Vp0 cos[θ0 ]
w2 (n) = Vp0 sin[θ0 ]
w3 (n) = Vdc
Vdc
w4 (n) =
τ
x1 (n) = sin[2πf0 n∆T ]
x2 (n) = cos[2πf0 n∆T ]
w1 (n) = Vp0 cos[θ0 ]
w2 (n) = Vp0 sin[θ0 ]
w3 (n) = Vph cos[θh ]
w4 (n) = Vph sin[θh ]
x1 (n) = sin[2πf0 n∆T ]
x2 (n) = cos[2πf0 n∆T ]
x3 (n) = 1
x3 (n) = sin[2πfh n∆T ]
x4 (n) = cos[2πfh n∆T ]
x4 (n) = −n∆T
Substituting above values in (5), we get,
Substituting above values in (2), we get,
y(n) = x1 (n)w1 (n) + x2 (n)w2 (n)
y(n) = x1 (n)w1 (n) + x2 (n)w2 (n)
+x3 (n)w3 (n) + x4 (n)w4 (n)
+x3 (n)w3 (n) + x4 (n)w4 (n)
(3)
which is simply a linear weighted combination of inputs.
Once the weights of the filters are estimated the amplitude
and phase of the fundamental harmonic and the amplitude
and time constant of the decaying dc can be estimated with
which is simply a linear weighted combination of inputs.
Once the weights of the filters are estimated the amplitude
and phase of harmonics and interharmonics can be estimated
5
3
Each agent uses the estimates of other agents and then tries
to maximize its information from the residual using same error
minimization algorithm. That in combination minimizes the
total residual error. That is a global emergence occurs by thier
localized self-interested behaviour.
This is similar to resource allocation problem where each
agent can only consume a resource upto its capacity. Here
when all agents have solved thier own problems the convergence is the total minimization of error. The model of the
agents constantly adapts to the measurement and with each
iteration the prediction gets better and better. In this paper
each agent uses algorithm based on method introduced in [8].
Nature has evolved biological systems that simple agents to
solve a complex problem adaptively and speedily. Consider a
biological framework of neuroscientist Donald MacKay, who
in 1956 proposed that the visual cortex is fundamentally a
machine whose job is to generate a model of the world. He
suggest that primary visual cortex constructs an internal model
that allows it to anticipate the data streaming up from the
retina. The cortex sends its predictions to the thalamus, which
reports on the difference between what comes in through the
eyes and what was already anticipated. The thalamus sends
back to the cortex only that difference information, the error
signal as is called in engineering paradigm. This unpredicted
information adjusts the internal model so there will be less of a
mismatch in the future. That is the model adapts to better represent the world which it sees or rather senses. In this way, the
brain refines its model of the world by paying attention to its
mistakes. Ceaselessly learning it gets better and better. Mackay
pointed out that this model is consistent with the anatomical
fact that there are ten times as many fibers projecting from
the primary visual cortex back to the visual thalamus as there
are going the other direction– just what youd expect if detailed
expectations were sent from the cortex to the thalamus and the
forward-moving information represented only a small signal
carrying the difference or error. In 1982, Marr’s human vision
model gave a computational theory to Human stereo vision [9].
In it the human perception was considered to be decomposing
the signal or image in a set of independent frequency channels
and then finely analysing it. So the brightness and saturation
are also affected by this fixed frequency resolution framework.
Even memory colors affects the frequency or color discerned
in images by a robust mechanism of human vision system
called color constancy[10].
Similarly in human audio system, it is worth noting that
estimating all three sinusoidal parameters, amplitude, phase
and frequency, is paramount for discerning high quality music. The human perception of a song or piece of music is
closely linked to the way different sources and thier respective
partials interact, and such an interaction strongly depends on
those parameters. Exact spectral coincidence is usually highly
unlikely due to the different characteristics of instruments and
musicians, and, if it occurs, it will just last for a few milliseconds [11]. So any algorithm aiming to seperate the signal
must be able to deal with close frequencies too. However this
frequency resolution cannot have arbitrary precision, it will
be constrained by acquisition and processing delays of the
system.
the following equations:
p
Vp0 = w1 (n)2 + w2 (n)2
w2 (n)
θ0 = arctan
w1 (n)
Vdc = w3 (n)
w3 (n)
τ=
w4 (n)
III. S OLVING L INEAR F ILTERING P ROBLEM
BASED M ODEL
USING
AGENT
Consider (3) a linear combination of inputs with additive
noise η,
Let,
y1 (n) = x1 (n)w1 (n) + x2 (n)w2 (n)
y2 (n) = x3 (n)w3 (n) + x4 (n)w4 (n)
y(n) = y1 (n) + y2 (n) + η(n)
We see that once the linear filtering approach is taken,
the linearly seperable problem can be further agentisized.
Now each agent can be given an input that is the measured
signal minus the output from other agents. That is agent 1
has input, yˆ1 (n) = y(n) − y2 (n) and agent 2 has input,
yˆ2 (n) = y(n) − y1 (n) as shown in Fig 1. This way each
agent can operate parallely and the algorithm would require
smaller number of samples per innovation compared to original problem.For instance, for B-LMS introduced in [8] to work
for (1) we require at least L samples of measured signal to
proceed with the algorithm where the value of L depends on
the number of frequency components we are seeking. Now if
we agentisize the problem and divide it into L/2 agents, only
two new samples are needed per innovation for the algortihm
to generate individual agents estimates. Hence it has a potential
to track dynamically the amplitude and phase drift faster. This
is a novel divide and conquer way of solving linear filtering
problem.
In this agent based modelling each agent will have a
designated known frequency value. There will be two weights
defined as in (2) for each frequency component. Using the
trignometric expansion we orthogonalize the components into
sine and cosine components as shown in (3). Once the two
weights have been computed , each agent would know its own
frequency component’s amplitude and phase. When all agents
have maximized thier orthogonal sine and cosine components
of specific frequencies the total residual error would have
minimized.
The steps or three stages of estimation are:
1. Competition
Each agent tries to maximize its own signal component
using some algorithm by minimizing difference between its
output and the input signal i.e Total measured minus outputs
of each agent which is initially zero for all agents.
2. Sharing
All agents after thier windowed period share thier information , that is their estimates of sine and cosine components.
3. Cooperation
6
4
Thus, in our modeled system, a combination of agents
tracking desired harmonics, interharmonics and dc offset can
then be used simply to solve a phasor estimation problem only
from the measurements of composite signal. Also using this
approach the computational complexity is reduced per agent,
the response is speedy and the distributed archiecture provides
more robust algorithm. The block diagram of Agent based
model to solve linear filtering problem is shown in Fig 1.
Measured Signal
y(n)
Agent 1
Agent 2
Fig. 1.
y1(n)
eL (n) = yL (n) − xTL (n)w(n)
where yL (n) = [y(n), y(n − 1)...y(n − L)]
xL (n) = [X(n), X(n − 1)...X(n − L)]
X(n) = [x1 (n), x2 (n − 1)...xK (n)]
w(n) = [w1 (n), w2 (n − 1)...wK (n)]
(6)
are the output, input and weight vectors. For simplicity,
henceforth the subscript L will be dropped from notation.
The mean square error (MSE) signal or the cost function is
given by,
1
(7)
E[w(n)] = eT (n)e(n)
L
Differentiating (5) w.r.t to weight vector w(n) yields,
Residual
Error
e(n)
2
∂e(n)
∂E[w(n)]
= e(n)
∂w(n)
L
∂w(n)
y2(n)
Hence the negative gradient vector is given by,
The Agent based model for solving linear filtering problem
−
The block diagram for each agent using a linear adaptive
filter to estimate phasors quantities is shown in Fig 2.
∂E[w(n)]
2
= xT (n)e(n)
∂w(n)
L
(8)
Update of the filter coefficients is done proportional to
negative of gradient according to the following equation:
2 T
x (n)e(n)
(9)
L
where η is the step size or learning parameter and
ŵ(n), ŵ(n + 1) represent the initial and the new estimates
of the weight vectors respectively.
The feedback loop around the estimate of the weight vector
ŵ(n) in the LMS algorithm acts like a low pass fitler,
passing the low frequency components of the error signal and
attenuating its high frequency components. Also unlike other
methods the LMS algorithm doesnt require the knowledge of
the statistics of the environment. Hence it is sometimes called
stochastic gradient algorithm. In precise mathematical terms,
the LMS algorithm is optimal in accordance with the H ∞ (or
minimax) criterion [13].
ŵ(n + 1) = ŵ(n) + η ·
Fig. 2.
The Adaptive system model for each agent
B. Conjugate Gradient Method
IV. A LGORITHM
We know that the error surface (MSE) is quadratic in weight
vector from (7). If an algorithm uses fixed step sizes to update
weights in (9) it would be a first order optimization steepest
descent method. It may need a large number of iterations
leading to slow convergence for some quadratic problems.
The conjugate gradient method tries to overcome this issue. It
belongs to a class of second order optimization methods collectively known as conjugate-direction methods[14]. Consider
minimization of a quadratic function f (w) :
USED FOR EACH AGENT
A. B-LMS algorithm
B-LMS or block least mean square error algorithm is
extensively applied in numerous signal processing areas such
as wireless communications, statistical, speech and biomedical
signal processing [12]. The B-LMS algorithm provides a
robust computational method for determining the optimum
filter coefficients (i.e. weight vector w). The algorithm is
basically a recursive gradient (steepest-descent) method that
finds the minimum of the MSE and thus yields the set of
optimum filter coefficients. The instantaneous error signal at
instant n processed in blocks of length L and weights of size
K for a linear system is given by,
1 T
w Aw − bT w + c
2
where w is a L-by-1 parameter vector, A is a L-by-L
symmetric, positive definite matrix, b is a L-by-1 vector, and
c is a scalar. Minimization of the quadratic function f (w) is
achieved by assigning to w the unique value,
f (w) =
w∗ = A−1 b
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5
Thus minimizing f (w) and solving linear system of equations Aw∗ = b are equivalent problems.Given a matrix A, the
set of nonzero vectors s(1), s(2), .s(L) is A-conjugate if:
Step 1:For n = 0, 1, 2 · · · and for a block size of length L,
and weight vector size of K, we have,
Input signal x(n) = [X(n) X(n − 1)...XL (n − L)]T
Measured signal y(n) = [y(n) y(n − 1)...yL (n − L)]T
Error signal e(n) = y(n) − xT (n)w(n)
Initialize weights ŵ(0) = [0 0...0]K
Gradient search direction:
sT (n)As(j) = 0
f or all n and j such that n 6= j
For a given s(1), s(2), .s(L) the corresponding conjugate
direction for the unconstrained minimization of the quadratic
error function f (w) is defined by:
s(0) = r(0) = −
w(n + 1) = w(n) + η(n)s(n)
n = 1, 2, 3 · · · L
Step 2:Find the optimal step size scalar parameter as used in
[8],
eT (n)xT (n)s(n) + sT (n)x(n)e(n)
η(n) =
2sT (n)x(n)xT (n)s(n)
(10)
where s(n) is the gradient direction and η(n) is a scalar
defined by,
Step 3:Update the weight vector
f [w(n) + η(n)s(n)] = min f [w(n) + ηs(n)]
η
ŵ(n + 1) = ŵ(n) + η(n)s(n)
This is a one dimensional line search for fixed n. The
residual of the steepest descent direction is,
Step 4:Find the new gradient direction
r(n) = b − Aw(n)
r(n + 1) = −
Then to proceed to the next step we use a linear combination
of r(n) and s(n − 1), as shown by the following equation:
β(n + 1) = max
(11)
rT (n)[r(n) − r(n − 1)]
rT (n − 1)r(n − 1)
rT (n)[r(n) − r(n − 1)]
rT (n − 1)r(n − 1)
Step 6:Update the direction vector
where the scaling factor β(n) is given by Polak-Ribiere
formula [14].
β(n) =
2
∂E(ŵ(n + 1))
= e(n + 1)x(n + 1)
∂ ŵ(n + 1)
L
Step 5: Use the Polak-Ribiere formula to calculate β(n + 1):
s(n) = r(n) + β(n)s(n − 1)
n = 1, 2, 3 · · · L
2
∂E(ŵ(0))
= e(0)x(0)
∂ ŵ(0)
L
s(n + 1) = r(n + 1) + β(n + 1)s(n)
Step 7:Set n = n + 1, go back to step 2
If the mean square error (MSE) E(w) is quadratic function
of weights,the optimal value of weights will reach in at most
K iterations where K is the size of the weight vector w.
(12)
Thus, conjugate gradient methods do not require any matrix
inversions for solving linear system of equations and are faster
than first order approximation methods. In combination with
the B-LMS algorithm they provide a very efficient way to
solve quadratic problems.
V. P ERFORMACE
RESULTS
In this section, the performance of the algorithm is evaluated
under two test conditions covering static state and dynamic
state test and the results are compared with conventional DFT
methods and latest published techniques in [5],[17], [18], [20],
[21], and [6]. All tests are performed with sampling rate N =
120 samples per cycle (i.e., sampling frequency = 7.2 kHz)
and a block size varies depending on number of weights to
be computed and number of iteration used , if any, is equal to
the number of weights. The higher sampling rate is useful for
high accuracy. Clearly since the algorithm used is same as in
[8] that static performance is similar.
C. Proposed B-LMS with conjugate direction search based
adaptive system for each agent
The block diagram for a linear adaptive filter to estimate
phasors quantities for each agent is shown in Fig 2. The
weights w are defined such that they trace the unknown
parameters, amplitude and phase of the frequency components.
Thus the unknown linear system has weights reflecting the
amplitude and phase of each component. The method helps
the adaptive system incrementally to match the output
of the unknown system corrupted with noise. The input
vector x takes on the modeled values based on timestamp
and frequencies while the desired vector y is the actual
measurement vector of the composite signal. The B-LMS
with conjugate gradient algorithm tries to track the unknown
weight vector by matching the outputs of the adaptive and
the unknown system through minimizing the error signal
generated between the two in presence of noise. The noise
need not be white Gaussian.
The steps of the B-LMS algorithm with conjugate gradient
search for the linear adaptive system are presented below:
A. Dynamic Step and Ramp Change Test using single agent
To evaluate the dynamic response when exposed to an
abrupt signal change, a positive step followed by a reverse
step back to the starting value under various conditions is
applied to the amplitude and phase angle of a sinusoidal
signal, respectively. The model used is using single agent
and to demonstrate the speedy response. Studies indicate that
under both types of steps, the amplitude and phase change,
the algorithm shows similar dynamic behavior. Here we used
a block size of 12 samples since only two weights are to
8
6
Fig. 3.
Fig. 4.
Fig. 5.
Dynamic response for the amplitude step
Dynamic response for the with amplitude step with prefiltering
Fig. 6.
Dynamic response for the phase step
Dynamic response for the amplitude ramp change
[5],[17] and faster than instantaneous sample-based methods
[18], [20] that require full cycle of fundamental component
about 16.66 ms. A dynamic amplitude response for a ramp
change is also done. The ramp occurs at 0.02 s and continues
to steadily increase till 0.06 s then it drops back to the original
value as shown in Fig 6. It is clear that the algorithm tracks
the constant changes steadily and the drop is tracked just in
1.67 ms. The performance of the algorithm showed similar
result in phase test.
be computed (i.e. .1 cycle). The results of the amplitude
step (10% of normal value) and phase step (π/18 rad), are
presented by Figs. 3-5, respectively without any iterations
used for blocks of data. The steps occur at 0.02 and 0.06
s. One can observe that the outputs track the changes in
the inputs extremely fast. It took 1.39 ms and 1.94 ms to
fully track the amplitude step change and 1.67 ms and 1.81
ms to track phase step change that occurred at two different
times respectively. To investigate the effect of prefiltering on
the algorithm dynamic performance, a third order Butterworth
low-pass filter with a cutoff frequency of 320 Hz is used to
process the input signals. Fig. 5 shows the result of amplitude
step test. Compared to Fig. 3, which shows the transient
behavior without signal prefiltering, one can see that the low
pass just slows the response from 3 to 5 ms with no significant
overshoot and undershoot and it is still less complex than
the RWT-based method [6] that takes about a quarter cycle
of fundamental component time period, DFT-based methods
B. Dynamic test using two agents
To evaluate the dynamic response when exposed to an
abrupt signal change occurs in one agent and the other agents
signal remains unchanged we used two agents model. The
results were as expected. Lowering the sample window size
using two agents working in parallel nicely isolates the perturbation in signal. The fundamental frequency agent’s follows
similar dynamic change while the second frequency agent’s
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A high frequency resolution could be achieved using this
model based technique by appropriately modeling weights.
The decaying dc component can be completely removed using
this technique. The performance of the algorithm is evaluated
under a variety of conditions that includes static test and
dynamic test. Comparison with other techniques demonstrates
the advantage of using this approach. The computational
burden is minimal when compared to non-linear or second
order methods or wavelet based methods; accuracy is high
and response is very rapid to satisfy time-critical demand of
the real time applications in power system. This model can
be easily adapted to drifts in nominal frequency when it is
known.
This is one of the most efficient time domain methods.
In power systems, as is well known, frequency is much
more tightly regulated parameter than amplitude and phase
of various signal components, where this technique can be
productively employed. Using agent based method further
improves the response since smaller number of samples is
needed per innovation. Hence in a dynamic enviornment it
would be very useful. However the algorithm using agent
based is more error prone. In sense that it takes longer time
to stabilize, since an error in estimation of one agent will
affect other agents and it will cycle in the algorithm and would
take longer than the conventional method to settle. It must be
emphazised that the local algorithm plays an important role
in determining the collective efficiency of agents. So further
research is required to try this distributed agent based scheme
using different local algorithm for agents and also to estimate
the nominal frequencies and its drift using some efficient
approach and combining it with this filtering algorithm.
Fig. 7. Dynamic response of amplitude of the agent 1 with fundamental
frequency
R EFERENCES
[1] I. Kamwa and R. Grondin, ”Fast adaptive schemes for tracking voltage
phasor and local frequency in power transmission and distribution systems”, in Proc. IEEE Power Eng. Soc. Transm. Distrib. Conf. , Dallas,
TX, 1991, pp. 930-936.
[2] A. A. Girgis and W. L. Peterson, ”Adaptive estimation of power system
frequency deviation and its rate of change for calculating sudden power
system overloads,” IEEE Trans. Power Del. ,vol.5,no 2, pp. 585-597, Apr
1990.
[3] K. M. El-Nagger and H. K. M. Youssef, ”A genetic based algorithm for
frequency relaying applications,” Elect. Power Syst. Res., vol. 55, no. 3,
pp. 173-178, 2000.
[4] L. L. Lai and W. L. Chan, ”Real time frequency and harmonic evaluation
using artificial networks,” IEEE Trans. Power Del. ,vol. 14, no 1, pp.
52-57,Jan. 1990.
[5] T. S. Sidhu and M. S. Sachdev, ”An iterative technique for fast and
accurate measurement of power system frequency,” IEEE Trans. Power
Del., vol 13, no. 1, pp. 109-115, Jan. 1998.
[6] J. Ren and M. Kezuovic, ”Real-Time Power system frequency and phasors
estimation using recursive wavelet transform,” IEEE Trans. Power Del.
,vol. 26, no 3, pp. 1392-1402,Jul. 2011.
[7] Iman Sadinezhad and Vassilios G, ”Monitoring Voltage Disturbances
Based on LES Algorithm, Wavelet Transform and Kaman Filter,” 35th
IEEE Industrial Electronics,IECON09., pp. 1961-1966, Nov 2009.
[8] S. Alam, “A New Fast Algorithm to Estimate Real Time Phasors using
Adaptive Signal Processing,” IEEE Trans. Power Delivery, Under Review.
[9] D. Marr, Vision,New York; Freeman, 1982.
[10] AC Hurlbert and Y. Ling, If it’s a banana, it must be yellow: The role
of memory colors in color constancy, Journal of Vision, 2005.
[11] J. G. A. Barbedo and A. Lopes, “Estimating Frequency, Amplitude and
Phase of. Two Sinusoids with Very Close Frequencies”, World Academy
of Science, Engineering and Technology 35 2009.
Fig. 8. Dynamic response of amplitude of the agent 2 with second frequency
signal remains unchanged. We see a very fast tracking of the
jump occuring at 0.02 s and a drop at 0.06 s for the agent
1 assoicated with fundamental frequency as shown in fig 7.
Second agent’s plot is shown in fig 8. Although we do see
ripples, the algorithm does a good work in mean-squared error
sense.
VI. C ONCLUSIONS
The paper introduces a new agent based adaptive filtering
approach to solve the problem of phasor estimation when
the frequencies of components are known. The algorithm
features very fast response and accuracy is good in meansquare sense. It uses less than a quarter cycle of fundamental component signal to estimate amplitude and phase
for a signal contaminated with harmonics or interharmonics.
10
8
[12] Ying Liu, Raghuram R, Matthew T and Wasfy B. Mikhael, ”Conjugate
Gradient based complex Block LMS employing Time-varying optimally
derived step sizes”,52nd IEEE International Midwest Symposium on
Circuits and Systems , pp.590-593, 2009
[13] B. Hassibi and T. Kailath, Mixed least-mean-squares/H-infinity-optimal
adaptive filtering, Proceedings of the 30th Asilomar Conference on
Signals, Systems and Computers , Pacific Grove, CA, Nov 1996
[14] Simon Haykin, Neural Networks, A Comprehensive Foundation, Prentice Hall, New Jersey,1996.
[15] Math H.J. Bollen and Irene .Y.H. Gu, Signal Processing of Power
Quality Disturbances , IEEE, Wiley, 2006.
[16] IEEE Standard for Synchrophasors for Power Systems ,IEEE Std.
C37.118-2005,Mar. 2006.
[17] D. Hart,D. Novosel, Y. Hu, B. Simth and M. Egolf, ”A new frequency
tracking and phasor estimation algorithm for generator protection,” IEEE
Trans. Power Del. , vol. 12,no. 3,pp. 1064-1073,Jul. 1997.
[18] M. D. Kusljevic, ”Simulataneous frequency and harmonic magnitude
estimation using decoupled modules and multirate sampling,”IEEE Trans.
Instrum Mes. , vol. 59,no. 4,pp. 954-962,Apr. 2010.
[19] A. Lopez, J. C. Montano, M. Castilla, J. Gutierrez, M. D. Borras, and
J. C. Bravo, ”Power system frequency measurement under non-stationary
situations,” IEEE Trans. Power Del. , vol. 23,no. 2,pp. 562-567,Apr. 2008.
[20] S. R. Nam, J. Y. Park, S. H. Kang, and M. Kezuovic, ”Phasor estimation
in presence of DC offset and ct saturation,” IEEE Trans. Power Del.,vol.
24, no 4, pp. 1842-1849,Oct. 2009.
[21] Y. Gou and M. Kezuovic, ”Simplified algorithms for removal of the
effect of exponentially decaying DC-offset on the Fourier algorithms,”
IEEE Trans. Power Del. ,vol. 18, no 3, pp. 711-717,Jul. 2003.
PLACE
PHOTO
HERE
PLACE
PHOTO
HERE
Syed Alam Abbas recieved his B.E degree from
University of Mumbai, in 2007, and is currently pursuing PhD degree at University of Central Florida,
FL, USA.
His research interests are developing new algorithms using signal processing and optimization
techniques and their applications in power system
protection, measurement, instrumentation and control as well as new areas in smart grid research.
Ivan Garibay is director and research faculty at
ORC, University of Central Florida, FL, USA.
His research interests include evolutionary computation, complex systems, economic modeling,
computational social sciences, and game theory.
11
An Agent-Based Model of Ant Colony Conflict
Charles Snyder
University of Central Florida
charles@knights.ucf.edu
November 26, 2012
Abstract
An agent-based model emulating conflict between two ant colonies is
presented. Though behavior of a single ant colony has been the inspiration for the ant colony optimization heuristic, there appears to be no
work towards a multiple-colony model. The presented model is found to
display characteristic behavior similar to actual ant colonies in foraging
and conflict dynamics, and we examine how this behavior is affected by
changes in parameters.
1
Introduction
The ant colony optimization heuristic was motivated by observations of the
behavior of actual ant colonies in their search for food - through the use of
many simple ants and stigmergy (communication through pheromones in the
environment) the colony is able to explore the environment and gather food.
Ant colony optimization emulates this behavior in order to find probabilistically
good solutions. The technique is commonly applied to problems that are similar
to shortest path in a graph, such as the travelling salesman problem - analogous
to finding short routes to food - or resource allocation, such as the knapsack
problem - analogous to division of ant labor across multiple food sources.
If a computational model of a single ant colony can provide such a useful
heuristic, what about a model of multiple colonies? In this paper, we extend the
classical single-colony agent-based model to include two conflicting colonies. It
is the intention of this paper to provide an accurate agent-based model of two
ant colonies to serve as a base for other studies.
2
Background
Ant colony optimization is a popular heuristic developed in the field of swarm
intelligence. The technique draws inspiration from the behavior exhibited by
real ant colonies in the search for food. As in many multi-agent systems, the
behavior of ants is dictated by simple rules and local communication. When an
1
12
ant colony forages for food, many ants wander into the environment in what is
essentially a random search. If an individual ant finds food it returns to the
colony, leaving a trail of pheromones along the way; other ants can then follow
this pheromone trail to help gather from the food source more efficiently. As
the pheromones will naturally diffuse throughout the environment and evaporate
due to heat and wind conditions, longer paths to food will eventually disappear
while shorter paths are adequately reinforced by the constant activity - in this
way ant colonies establish and maintain a short path to available food sources
[3]. Though the ants’ brains are individually simple, by storing information
in the environment through pheromones as a means of communication the ant
colony as a collective is able to self-organize, optimize its resources towards food
gathering, and establish reasonably short paths through the environment.
Taking this example of self-organization in nature as a model, Dorigo proposed ant colony optimization as a swarm-intelligence-based, probabilistic heuristic for problems similar to finding a shortest path in a graph [2]. Dorigo’s
method captures the essentials of stigmergy by having better solutions acquire
more pheromone per step than less optimal solutions, while candidate solutions
are formed by weighted random choice biased towards the previously found
solutions with larger amounts of pheromone.
Some previous agent-based models have used ant colony optimization as a
base. There have been several studies [4, 9, 10] that use agent-based ant colony
optimization to design manufacturing workflows. In these models different types
of food represent the different raw materials and products of the manufacturing
process, and different ant nests represent stations that exchange input materials
for output materials. The ants of these models serve to establish materials
transport routes through the work floor from input raw materials to station,
from station to station, and from station to output areas. After some amount of
simulation time, areas of high pheromone concentration are selected as material
routes. As one might expect - given the similarity of this task to that of finding
a shortest path in a graph - the agent-based ant colony simulations performed
this task well.
Agent-based models similar in spirit to the proposed competitive colony
model have been investigated, though none use ant-like stigmergy. One such
model investigates tribes of East African herders in competition for grazing
land and watering holes [5]. As in the ant colony model, herders must travel
from watering holes to suitable grazing land and back to their water source,
and herders can directly battle for control of pastures. Unlike the ant colony
model however, the herders of a single tribe do not communicate with each
other directly or indirectly, but instead pool their resources together. The experimenters note that the eventual rise of one tribe to dominance seems to be
an inevitability, though certain conditions tend to prolong this event.
2
13
3
Model
The NetLogo library is furnished with a single-colony model [12]; for consistency
we adapt some of the single-colony behaviors to the two-colony model. Individual ants navigate by sampling the patch straight ahead, the patch ahead and to
the left, and the patch ahead and to the right, then turning towards the patch
with the highest amount of pheromone. At each time step an ant randomly
changes direction by turning up to 40 degrees in either direction and moves
forward 1 unit. Upon finding food an ant will navigate back to its nest using a
sort of internal compass - at each point the ant knows which neighboring patch
is closest to the nest, and the ant moves accordingly. This approximates several
common methods of ant navigation, such as internal tracking [13], visual recognition [6], and magnetic navigation [1]. On its return trip, the food-carrying ant
will leave a trail of pheromone that other ants can then follow.
A key difference between the single- and dual-colony models is the allocation
of food. While the single-colony model starts with 3 static piles of food, the
dual-colony model replaces food once it has been gathered to emulate the growth
and appearance of food in the ants’ habitat and to allow for longer observation.
Food is randomly placed in piles of 20 units into the environment; once 20 units
of food have been gathered by the ant colonies, another pile of 20 is introduced.
The addition of a second ant colony to the model necessitated a few design
decisions. The first concerns how to accommodate a second colonys pheromone
trails: for simplicity we say that each colony has a separate pheromone, but
other than their colony associations the pheromones are identical to avoid giving
either colony an unintended advantage. Ants of one colony are unable to identify
or process the pheromone trails of the opposing colony.
The second decision concerns the process of conflict between two individual
ants. Each ant is given an aggression factor - randomly distributed between
0 and 100 - indicating how often the ant will attack an ant from the opposite
colony when one is nearby; an aggression of 0 indicates the ant will never attack
an opposing ant, while an aggression of 100 indicates the ant will always attack.
An attack simply consists of moving to the targeted ant in 1 step and removing it
from the environment. When an ant dies it releases a large amount of pheromone
to indicate a threat to the colony and to attract surviving ants for colony defense
- in this model this pheromone is the same as the one used for foraging.
The colonies can add to their numbers by gathering food: after a predetermined amount of food is gathered by a single colony, that colony produces an
additional ant worker. Since ants only die as a result of conflict, this method of
replacement is intended to approximate the life and death cycle caused by age,
starvation, and outside entities/forces.
4
Experiment
The behavior of the model is observed under varying initial populations, pheromone
volatility (diffusion and evaporation rates), and food availability. We measure
3
14
Figure 1: Visualization of the model.
the amount of time before either colony is extinct, if such an event occurs.
It is expected that initial population size will have little effect on survivability. In the case of large initial populations the colonies will be able to effectively
organize paths to food and reproduce from the start, however the abundance
of ants will lead to extreme conflict. The case of small initial populations is
expected to behave the same but for opposing reasons: colonies will not be able
to reproduce quickly because of their inability to self-organize, but the lowered
density of ants in the environment will lead to fewer conflicts and fewer deaths.
Pheromone volatility is expected to have a more significant impact. At low
volatility the colonies will be able to establish strong routes to food, and so the
ants will be drawn to these routes rather than wandering into opposing territory. At high volatility these routes cannot be established and so the ants are
reduced to random wandering, causing a more even spread of ants throughout
the environment and so more conflict.
The availability of food is expected to cause the most significant impact
on survivability. With few piles of food in the environment both colonies will
congregate in a small space, causing a higher rate of conflict and eventually
extinction. However when food is abundant there is little reason for overlapping foraging routes, so conflict will be relatively rare compared to the rate of
gathering and both colonies will survive much longer.
4
15
Figure 2: Extinction time with 10% evaporation rate and 120 units of food.
Initial population varies between 60, 120, and 180 ants.
5
Results
Parameter settings of 120 initial ants, a 10% evaporation rate, and 120 units of
food (6 piles) in the environment produced behavior qualitatively similar to that
described in [11, 8, 7], so these settings are used as a base and the individual
parameters are varied one at a time. Results are collected from 100 simulations
of each parameter set, and time to extinction of one colony is presented in
Figures 2, 3, and 4.
Initial population size was varied between 60, 120, and 180 ants (Fig. 2).
As expected, this variation had little effect on long-term survivability; it was
common to see widespread fighting in the early steps in an amount proportional
to the population size - larger initial populations result in more ants wandering
before pheromone trails are established, which in turn results in more random
conflicts.
Pheromone evaporation rate was varied between 5%, 10%, and 15% per time
step (Fig. 3). Though a rate of 5% appears to allow for longer coexistence it
was observed that much of this time was spent tracing pheromone trails that
were exhausted of food - so while both colonies survived for longer they did
not gather food corresponding to this extra time. Despite the significantly
faster evaporation at 15% when compared to 10%, colony behavior was fairly
similar: though a rate of 15% was not low enough to maintain strong pheromone
trails (while 10% was low enough) it was enough to establish pheromone fingers
reaching from the nest towards the food source, providing other ants with a
direction in which to search.
The food abundance of the environment was varied between 60, 120, and
180 units (3, 6, and 9 individual piles of food respectively) (Fig. 4). As was
5
16
Figure 3: Extinction time with 120 initial ants and 120 units of food. Evaporation rate varies between 5%, 10%, and 15%.
Figure 4: Extinction time with 120 initial ants and 10% evaporation rate. Food
quantitiy varies between 60, 120, and 180 units.
6
17
Figure 5: Population over time of a typical run at 120 initial ants, 10% evaporation rate, and 120 units of food.
Figure 6: Amount of food collected over time for the same run as Fig. 5.
expected, increasing the amount of available food significantly increases the
time before a colony extinction due to the lack of competition and separation
of gathering routes (and the lack of deaths that result from those conditions).
6
Discussion
Several behaviors that characterize actual ant colony foraging and competition
are commonly observed in the model. The ability to establish gathering routes
to nearby food sources and quickly collect that food is central to any ant colony
system, and such behavior is constantly observed. To evaluate the extension
of the one-colony system to two colonies, we focus on the nature of conflict
observed in the new model.
In the early stages of the simulation - before food is found and pheromone
trails are established - ants wander randomly in the environment. This disorganization results in high rates of conflict when the wandering ants from opposite
7
18
colonies meet for the first time: the opposing ants spread evenly out from their
nests, so they meet at the geographic border between the nest territories, and
conflict erupts along the border. Border conflicts are also commonly observed
between colonies of desert ants [11]. The conflict spreads as ants are attracted
by the pheromones left by their dead comrades, until enough ants are killed
in conflict or drawn to pheromone trails to food such that the number of free,
randomly wandering ants is low enough to make colony collisions rare.
After enough time has passed to establish gathering routes and most random
wandering is replaced by pheromone-guided foraging, conflicts in empty spaces
nearly disappear as ants are drawn to direct paths to food. Instead conflict
occurs more often either close to the nests or around food sources.
Conflict at a nest results when a single (or few) foraging ant in search for
new food wanders into the opposing nest; it is likely that many opposing ants
are near the nest either in the process of bringing food or setting out to gather,
and so there is a high probability for conflict. Such behavior is observed among
established colonies of desert ants [11].
Conflict at food sources results when foraging ants stumble upon a food
source currently being harvested by the other colony - again because the opposing colony is guiding ants to the food source, and the high concentration
of opposing ants results in a high probability for conflict. Occasionally both
colonies can be seen briefly harvesting the same food source from opposite sides
if the foragers do not encounter each other, but more often than not one colony
will prevent the other from establishing a pheromone route by eliminating the
early foragers. This phenomenon results in colonies harvesting from different
food sources, a behavior clearly observed in the diet of competing desert ant
colonies in [7, 8].
7
Conclusions
By extending the typical single-colony agent-based model to two colonies, we are
able to reproduce several common behaviors found in real-life ant ecosystems.
In addition to the common foraging and path-finding between the nest and food
sources, the model demonstrates conflict dynamics observed during monitoring
colonies of desert ants [7, 8, 11]. Testing of individual parameters shows how
changes in behavior can be effected. We believe that the proposed model adequately captures qualitative behaviors of competing real-life ant colonies, and
that the model is easily extendable for both more general and more specific
studies of swarm intelligence.
Though beyond the scope of the developed model, it would be interesting
to observe colony behavior under a more intricate model of ant intelligence.
This would likely be accomplished through the use and processing of multiple
pheromones - many complex ant behaviors such as mimicry, cooperation, and
parasitism are possible through subtle manipulation of pheromones. Additionally more heterogeneity among the ants would likely produce social castes, which
would in turn result in more complex interactions.
8
19
References
[1] A. N. Banks and R. B. Srygley. Orientation by magnetic field in leaf-cutter
ants, atta colombica (hymenoptera: Formicidae). Ethology, 109(10):835–
846, 2003.
[2] M. Dorigo. Optimization, Learning and Natural Algorithms. PhD thesis,
Polytechnic University of Milan, 1992.
[3] S. Goss, S. Aron, J. L. Deneubourg, and J. M. Pasteels. Self-organized
shortcuts in the Argentine ant. Naturwissenschaften, 76:579–581, Dec.
1989.
[4] Hadeli, P. Valckenaers, M. Kollingbaum, and H. V. Brussel. Multi-agent
coordination and control using stigmergy. Computers in Industry, 53(1):75
– 96, 2004.
[5] W. G. Kennedy, A. B. Hailegiorgis, M. Rouleau, J. K. Bassett, M. Coletti,
G. C. Balan, and T. Gulden. An agent-based model of conflict in east africa
and the effect of watering holes.
[6] B. Ronacher and R. Wehner. Desert ants cataglyphis fortis use self-induced
optic flow to measure distances travelled. Journal of Comparative Physiology A, 1995.
[7] R. T. Ryti and T. J. Case. Field experiments on desert ants: Testing for
competition between colonies. Ecology, 69(6):pp. 1993–2003, 1988.
[8] N. J. Sanders and D. M. Gordon. Resource-dependent interactions and
the organization of desert ant communities. Ecology, 84(4):pp. 1024–1031,
2003.
[9] P. Valckenaers, Hadeli, B. S. Germain, P. Verstraete, and H. V. Brussel.
Mas coordination and control based on stigmergy. Computers in Industry,
58(7):621 – 629, 2007.
[10] P. Valckenaers, M. Kollingbaum, H. V. Brussel, and O. Bochmann. The
design of multi-agent coordination and control systems using stigmergy. In
In Proceedings of the third International Workshop on Emergent Synthesis,
2001.
[11] J. D. Vita. Mechanisms of interference and foraging among colonies of the
harvester ant pogonomyrmex californicus in the mojave desert. Ecology,
60(4):pp. 729–737, 1979.
[12] U. Wilensky. Netlogo ants model, 1997.
[13] M. Wittlinger, R. Wehner, and H. Wolf. The Ant Odometer: Stepping on
Stilts and Stumps. Science, 312:1965–1967, June 2006.
9
20
Effects of Wealth Distribution
In a Progressive Tax Model
By David Gross
1. Abstract
This project will study an artificial tax based model that successfully reproduces the behavior of
a countries tax system. To implement the tax model an agent based model is used with rules of
work and taxation behavior which its agents follow. The simulation will allow agents to acquire
money, consume money, pay taxes and die of starvation, migrate to other jobs, reproduce, and
compete with each other. To implement the economic flat tax and progressive tax model a
distribution of agents with disparate economic prospects will be used. Modification to the tax
bracket percentages and its effect on a Laffer type curve will be used to validate the taxation
model. Although the system resulting from the interactions of the agents with tax re-distribution
is not perfect replicas of more complicated economics this will lend insight into the effect of tax
policies on wealth distribution. The model allows for analysis of a variety of trends resulting
from tax policies among which is wealth distribution, and is a useful tool for economic science.
Keywords: agent based modeling, wealth distribution, tax model, Laffer curve, economic
science
2. Introduction
Agent based modeling is a useful tool for modeling complex situations and has become a useful
method for simulation in the fields of social and economic science. One common simulation
using agent based modeling is Sugarscape, designed by Epstein and Axtell. This model is
comprised of a set of agents who make collect sugar from a landscape that has an unequal
distribution of the sugar. The agents have a limited range of vision for detecting sugar in the
landscape and moving toward it. As the model progresses the agents continual to gather sugar
reproduce, and eventually die. Factors in the model like vision range and initial placement
creates an unequal distribution of sugar among the agents. In this paper a basic model of a tax
based society based off the original sugarscape model is created, in which the elementary
population who are the properly parameterized agents will be distributed in an artificial
economic environment. Then a self organized redistribution of wealth through income accrual,
taxation, living expense dispersal and welfare could be observed. Each parameterized
distribution defines a different script along with the overall population dynamicity with certain
emergence features. The difficult job is to choose valid economic parameters for achieving valid
distribution behaviors which are self-perpetuating in simulations. This has been done through
incorporating and adapting actual US economic data available from census databanks. The
objective of this research is to determine adequate parameters for an artificial society that can
model a tax based society based on the Laffer curve these types of societies follow.
21
In this model fundamental tax structures and group behaviors will be observed through
spatiotemporal interactions among agents as well as agents and artificial environment. Both
agents and the environment have spatial evolutionary rules and economic restrictions which are
defined by variable sets of parameters. The model will be built with three separate variations
simple tax, progressive tax and a welfare type distribution. In all likelihood one variation will
provide the equitarian wealth distribution.
3. Background
The application of agent based modeling, specifically Sugarscape, to study wealth distribution
and disparity has been undertaken by a number of researchers in economics and social sciences.
However, after extensive review of public papers no research was found for using it to study
taxation and its effect on wealth distribution. The authors Impullitti and Rebmann in an”An
Agent-Based Model of Wealth Distribution” used Netlogo to create a modified model of
Sugarscape to look at wealth distribution. They found that inheritance of non-biological factors
increased wealth distribution while inheritance of biologically based factors decreased it.
A 2011 report by the International Monetary Fund by Andrew G. Berg and Jonathan D. Ostry
found a strong association between lower levels of inequality and sustained periods of economic
growth. Developing countries (such as Brazil, Cameroon, Jordan) with high inequality have
"succeeded in initiating growth at high rates for a few years" but "longer growth spells are
robustly associated with more equality in the income distribution." (Ostry, April 8, 2011) The
Pigou–Dalton principle is that redistribution of wealth from a rich person to a poor person
reduces inequality but ignoring questions of economic efficiency: redistribution may increase or
decrease overall output. The Prospect of Upward Mobility (POUM) hypothesis is an argument
that voters do not support redistribute wealth. It states that many people with below average
income do not support higher tax rates because of a belief in their prospect for upward mobility
(Roland Benabou, May, 2001)
The parameters for the model will be based on US census data, economic brackets, percentages
and poverty levels. The U.S. Census Bureau breaks down the reported household incomes into
quintiles (or five divisions). In 2007, the middle quintile reported an income range of $36,000 to
$57,660. Many economists and politicians alike believe this range is too narrow to encompass
the true middle class of America. Therefore, a more generous range would include the middle
three quintiles, which makes the range from $19,178 to $91,705. This range accounts for 60
percent of all households, and with the lower end balancing near the poverty threshold, this range
may not be completely accurate.
Other behavior parameters will use survey summaries such as living cost percentages and
relative wage factors. Validation of the tax structure will be accomplished by recreating the
Laffer curve for tax revenue. In economics, the Laffer curve is a representation of the
relationship between government revenue raised by taxation and possible rates of taxation. It
illustrates the concept that taxable income will change in response to changes in the rate of
taxation. This is due to two interacting effects of taxation: "arithmetic effect" that assumes that
tax revenue raised is the tax rate multiplied by the revenue available for taxation. At a 0% tax
rate, the model assumes that no tax revenue is raised. The "economic effect" assumes that the tax
22
rate will have an impact on the tax base itself. At the extreme of a 100% tax rate, no tax is
collected because there is no incentive to working. Although the Laffer curve is a unproved
hypothetical concept a great deal of historical data examples (i.e. Russia and the Baltic states flat
tax, Kemp-Roth tax act, the Kennedy tax cuts, the 1920s tax cuts, and the changes in US capital
gains tax structure in 1997) give empirical evidence to support it.
4. Theory and Design
The model’s agent behaviors are specified by a set of guidelines. One of these guidelines
involves searching for income: in each time step, each agent determines which patch or patches
of the model would be the best place to move. This is done within each agent’s scope of vision, a
number specified by the economic bracket of the agent (usually between 1 and 10 patches). The
agent looks north, south, east, and west, in the scope of its vision and determines the patches
with the most money that is not already occupied by another agent. Then the agent randomly
selects one of the best patches and moves to that patch. This is done by each agent individually,
rather than simultaneously, to prevent two agents from occupying the same patch. The agent then
gathers the money on the square in increments equal to its income level adding it to the agent’s
savings. Each time cycle a percentage based on the agent’s economic bracket plus living cost is
subtracted from savings and added to an accumulator. At each time step, the agent may also
reproduce. This occurs based on a probability distribution based on the agent’s income level.
The new agent inherits the parent’s income level and sight range. At each time step, the agents
may also die. This happens either after 208 time steps (80 years) to simulate death due to age or
if an agent cannot maintain their living cost which simulates starvation.
Each time step, the amount of money in the accumulator is distributed to the patches
There are a number of variables that can be controlled by the user. Birth probability, income tax
rate, living expense, maximum vision, and the number of turtles at the beginning of the
simulation can all be set at the start. Income tax rate, living expense and maximum vision can
also be changed during the run of the program. While the turtles are moving throughout the
simulation, a number of different mathematical analyses run in the background and graphical
representations of these analyses are shown as well.
4.1 Behavior Assumptions and Simplifications
A number of assumptions and simplifications are developed for the model. The assumptions are
based on society studies and group behavior. The simplifications were done to keep the model
workable without effecting validity. The following were used:
 Tax payers are limited to finding work draws a paycheck and pays their taxes.
 People in a higher income have greater foresight (vision) in employment and higher
living expenses.
 Wealth distribution must include more than tax collection and disbursement (i.e. Trail
Taxes).
23
 Welfare distribution should be limited to the lower economic level and have a negative
(but minor) effect on work prospects.
 Comparison of simple and progressive tax models need to be evaluated both by revenue
and class burden.
4.2 Design Approach
The model will be based on a variation of the Sugarscape model (Axtell, October 11,
1996). Some other design considerations are: the agents themselves would be
classified following US Census guidelines (Quintiles) and will be the source of tax data
used. The behavior of agents to seek wealth and the amount they can acquire each
cycle will be tied to their income levels. The expenses level for agents each cycle will
also tied to their income level. Consistently high or low savings will shift agent’s income
level. The model of the system will be considered closed (i.e. no new wealth added) so
cell money levels will not regenerate. And both a central “accumulator” and “tax
collector” will collect money from agents for their living expenses and taxes. The money
collected in one cycle will be redistributed at the end of the cycle. In the welfare version
a percentage of the wealth will be given directly to agents with the lowest level of
savings (poor) as welfare.
This variation of the original Sugarscape will utilize three different algorithms to analyze
wealth distribution: the Lorenz curve, the Gini coefficient, and the Robin Hood index.
Both the Gini coefficient and the Robin Hood index are derived in relation to the Lorenz
curve, but they offer different information regarding wealth distribution.
The Lorenz curve can be used to show what percentage of a nation’s residents
possesses what percentage of that nation's wealth. Every point on the Lorenz curve
represents a percentage of population and the percentage of total income they possess.
A perfectly distribution of income would be where every person has the same income.
This would be depicted on the Lorenz curve by a straight line y = x. By contrast, a
perfectly unequal distribution would be one in which one person has all the income and
everyone else has none. In this case the curve would be y = 0 for all but one person
where it would be 100%.
24
The Lorenz curve can often be represented by a function L(F), where F is represented
by the horizontal axis, and L is represented by the vertical axis.
For a population of size n, with a sequence of values yi, i = 1 to n, that are indexed in
non-decreasing order ( yi ≤ yi+1), the Lorenz curve is the continuous piecewise linear
function connecting the points f(x), i = 0 to n, where F0 = 0, L0 = 0, and for i = 1 to n:
The Gini coefficient is a measure of statistical dispersion that is used in the analysis of
income distribution. It is a measurement that ranges from 0 to 1, with 0 being one
person owns everything and 1 where each person owns an equal share.
Mathematically it is the ratio of the area between the equal and unequal distribution
lines on a Lorenz curve. The Gini coefficient will be calculated with the formula
4.3 Design Concepts
The development tool selected was NetLogo (Wilensky, 1999) a model developer tool
for cellular automata. With this tool time is processed in steps and space is represented
as a lattice or array of cells (i.e. patches). The cells have a set of properties (variables)
25
that may change over time. There are agents which act and interact and have
properties and behavior that can be programmed. Use of this tool has resulted in the
following design concepts being implemented:
4.4 Rules
A number of rules on interaction of the agents have been derived to support the taxation. These
behaviors are rules are coded within the system as scripts and are as follows:
 Money collected but not spent is stored and taxed but with no upper limit on amount.
 Each agent can move only once during each round towards the largest payroll cell within
their vision.
 The agent harvest the money in their current cell and every cycle sends to the
accumulator an amount of money owed for expenses and to the collector for taxes.
 If at any time the agents savings drops below the expense level the agent dies and is
removed from the model
 New agents will be born and added to play based on a random selection of an existing
agent. New agent will inherit parent’s vision, appetite, and a split of their parent’s
savings.
4.5 Source Data
The model will require minimum and maximum ranges of income to determine economic class.
The US Census department use quintiles for their data groupings. Dividing a statistical group
into five categories is referred to as quintiles. For income that means that the minimum and
maximum income in each 20% range defines the class. The following is the data from the 2009
census.
Quintile
Min. Income
1st
$91,706
2nd
$61,802
Max. Income
Class
N/A Rich
$91,705 Upper Middle
26
3rd
$38,551
$61,801 Middle
4th
$20,454
$38,550 Low Middle
5th
$0
$20,453 Poor
Source: US Census Bureau, http://www.census.gov/hhes/www/income/
Consumer spending or consumer demand or consumption is also known as personal consumption
expenditure. It is the largest part of aggregate demand or effective demand at the macroeconomic
level. This model will use consumer spending to determine the cost of living expenditures for
each class. The following source data from Bureau of Labor Statistics consumer survey was
what was used.
Description
1st
2nd
3rd
4th
5th
Consumer Units (thousands)
24,435
24,429
24,473
24,520
24,430
Income before taxes
$9,805
$27,117
$46,190
$74,019
$161,292
Income after taxes
$10,074
$27,230
$45,563
$72,169
$153,326
Average annual expenditures
$22,001
$32,092
$42,403
$57,460
$94,551
Source: Bureau of Labor Statistics, http://www.bls.gov/cex/tables.htm
5. Experiments and Results
Money collected but not spent is stored and taxed but with no upper limit on amount.
Each agent can move only once during each round towards the largest money cell
within their vision. The agent harvest the money in their current cell and every cycle
sends to the accumulator an amount of money owed for taxes and expenses.
If at any time the agents savings drops below the expense level the agent dies and is
removed from the model Agents will die at a random number of rounds based on a
standard life length distribution. New agents will be born and added to play based on a
random selection of an existing agent. New agent will inherit parent’s vision, appetite,
and a split of their parent’s savings.
Quintile
1st
2nd
3rd
4th
5th
Min. Income
$91,706
$61,802
$38,551
$20,454
$0
Max. Income
N/A
$91,705
$61,801
$38,550
$20,453
27
Class
Rich
Upper Middle
Middle
Low Middle
Poor
Figure 1 - 2009 Census Income Data by Quintile
6. Results
An initial simulation was run using a grid size of 100 x 100 (10000 patches). The initial
distributed wealth was 30 million dollars in a random probability distribution of $1 to
$20,000 per patch (10% coverage). An initial level of 500 agents with 100 in each
quintile were created and dispersed on the grid. Each agent was given a vision and
income level consistent with demographic data for their quintile. All agents started with
savings equal to 4 months pay for their income level. The pay period used for all agents
is bi-weekly so each run was set to last for 52 ticks (2 years). This allows for one year
of tax revenue to be collected outside of the initial period of adjustment. To achieve a
confidence factor of above 95% a total of 100 runs for both simple and progressive
taxation for tax rates from 0% to 100% was completed. The data was averaged and
summarized below:
Tax Rate
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Simple
0
0
6.31
8.91
13.22
17.4
25.26
27.03
30.64
26.33
8.42
5.43
0.68
0
0
0
0
0
0
0
0
Simple Welfare
0.00
0.00
7.27
9.09
13.29
17.73
26.12
27.96
31.25
27.03
8.70
6.18
0.69
0
0
0
0
0
0
0
0
28
Progressive
0
0.88
9.28
11.98
16.56
18.25
23.9
28.89
27.32
22.06
5.63
0
0
0
0
0
0
0
0
0
0
Progressive Welfare
0.12
1.25
9.75
12.56
17.41
18.77
24.81
28.97
27.86
22.31
6.31
0.95
0
0
0
0
0
0
0
0
0
With the data collected a Laffer curve for each tax model could be created and
compared. Below are the results of that comparison. As shown both tax models
provided similar curves with a few minor differences. Primarily is in the height of the
peak or optimal revenue and a slight shift to the left or lower tax rate for the progressive
model.
7. Conclusions
Several possible conclusions could be drawn from this model. First that a Laffer curve can be
reproduced for both taxation systems. Second that although a shift and reduction of the Laffer
curve seems to occur for a progressive tax the difference was inconclusive given the confidence
factor of the data. Lastly that welfare disbursal for low income reduces inequality but at high
levels of disbursal can have a detrimental effect on overall income levels. One thing should be
kept in mine about these possible conclusions is that the model is heavily simplified and based
on an unrealistic tax model. There are numerous assumption and generalities in its design and
the source data, although official government based statistics shows conflicting information. The
one valid conclusion that can be drawn is the results are interesting, shows promise in answering
questions economist have been arguing about and that it should be considered a “proof of
concept”.
Several areas in which the model could be easily improved are in the incorporation of businesses
for both taxation and subsidy. Currently the model treats all tax sources as people without the
perks and special issues that businesses require. Second, opening the system to allow wealth to
enter and leave would simulate trade imbalance and the use of internal resources to generate
revenue. Third would be including the agent behavior of unemployment and unemployment
insurance. Lastly would be the separation of tax types and tax trails. Currently the model treats
29
all tax revenue like income tax. This is responsible for some of the issues in incorporating real
data into the model.
8. References
Axtell, J. M. (October 11, 1996). Growing Artificial Societies. Brookings Institution Press.
Ostry, A. G. (April 8, 2011). Inequality and Unsustainable Growth: Two Sides of the Same
Coin? IMF STAFF DISCUSSION NOTE.
Roland Benabou, E. A. (May, 2001). Social Mobility and the Demand for Redistribution: The
Poum Hypothesis. The Quarterly Journal of Economics.
Wilensky, U. (1999). Center for Connected Learning and Computer-Based Modeling. Boston:
Tufts University.
30
A New Measurement of Complexity
for Cellular Automata
Automata:: Entropy of Rules
Fan Wu
Department of Engineering and
Computer Science,
University of Central Florida
jayvan_fanwu@knights.ucf.edu
ABSTRACT
λ=
In this paper, Langton’s lambda coefficient measuring the
complexity of Cellular Automata has been reviewed. The lambda
coefficient is in fact not a good measurement since it treats
tranquil state (which is always represented as 0) more special than
any other state, while all possible states should be treated
symmetrically. Inspired from Shannon’s information theory,
another means to measure the complexity of Cellular Automata
has been proposed, which is the entropy of the rule table. Several
experiments regarding one-dimensional Cellular Automata with
different neighbor radius and states number have been conducted.
The experimental results show that Langton’s lambda coefficient
fails to measure the complexity of a 2-state Cellular Automaton
and doesn’t perform as well as we thought with 3 or more states
Cellular Automata. On the other hand, the Entropy of Rules
performs better in measuring complexity of a Cellular Automaton
in all the experiments. And it is clearly more consistent in all the
results than Langton’s lambda coefficient.
N − N0
N
In this equation, N represents the total number of rules for a CA,
and N0 represents how many of them have the next state of
tranquility (or state 0). However, all the possible states of a
Cellular Automaton are symmetric. Thus the tranquil state (state 0)
should not be treated differently from other states. A simple
example is that, CA I with all the rules having the next state of 0
has λ=0, and CAII has λ=1 while all of its rules have the next state
of 1. It is obvious that both CAs are not complex at all even
though they have the greatest difference on λ. So it is obviously
not true to say that Wolfram’s four categories lie on the lambda
axis in the exact order of static, cyclic, complex and chaotic in 2state Cellular Automata.
In this paper, I propose another way to measure the complexity of
Cellular Automata, which is also based on the rule table, but
determined by the entropy of the rules. Several experiments have
been designed and conducted to compare the performances of
lambda and the Entropy of Rules. The results unsurprisingly
showed that the Entropy of Rules is not only more consistent with
different CAs regarding Wolfram’s classification, but also
performs better in distinguishing the complex category from the
chaotic category than lambda.
General Terms
Measurement, Experimentation, Theory.
Keywords
Cellular Automata, complexity, lambda coefficient, entropy.
The rest of this paper is organized as follows: the second part
introduces the Entropy of Rules in a formal way and theoretically
compares it with Langton’s lambda coefficient. The third part
depicts the details of the experiments and shows the results. The
last part is the conclusion about the newly proposed measurement
for complexity, Entropy of Rules. Its weaknesses are also
included in this part as well as how should future work overcome
the weaknesses.
1. INTRODUCTION
Von Neumann’s proposal of Cellular Automata(CA) has inspired
a lot of researchers to use this powerful model to simulate several
real world systems, some of which have got encouraging results.
One of the famous models is Conway’s Game of Life. In this
model, people can generate different interesting phenomena and
show how complexity the model can be. One of the interesting
result is that it can construct negative gate, AND gate and OR gate
by placing “Glider Guns” in proper places in a Cellular
Automaton. This is important because if one can construct these
gates, he/she can construct a universal computer. That is to say,
CA has the ability of universal computing. In 1980s, Wolfram
classifies CAs with different rules into four categories, among
which the complex category concerns us most. Wolfram also
pointed out that Rule 110 on 1-Dimension CA with just two
closest neighbors creates complex and interesting patterns, so it is
classified into the complex category. Later around 2000, Matthew
Cook proved that Rule 110 is Turing complete, i.e., capable of
universal computation. This is why people are always interested in
CAs classified into the complex category.
2. ENTROPY OF RULES
Let’s review Langton’s lambda coefficient, it actually measures
the possibility of a non-tranquil next state given an arbitrary state
and its arbitrary neighbors, by measuring the number of rules
having a non-tranquil next state. However, as mentioned before,
each possible state should be treated symmetrically. That is to say,
we should not only measure the frequency of non-tranquil states
in the rule table but the frequencies for all possible states, say
pi =
However, measuring complexity of a Cellular Automaton is not
easy. Langton introduced the lambda coefficient around 1990 to
measure the complexity[4]:
Ni
N
,
Ni is the number of rules having next state of i. If a CA has k
possible states, then i can take the value from 0 to k-1. Recall the
definition of Shannon’s entropy, we can derive the entropy of the
rules:
31
Cellular Automaton has two possible states of {0, 1}, the rule
table of the Cellular Automaton is showed in Table 1. Then we
can calculate Langton’s lambda coefficient as λ=5/8=0.625. On
the other hand, because of p0=3/8 and p1=5/8, the Entropy of
Rules should be ER = – p0 log p0 – p1 log p1 =0.954.
k −1
E R = −∑ pi log k pi
i =0
In this equation, ER measures not only the entropy of the rules, it
also measures how chaotic the CA could be. For instance, if all
the rules have the same next state, i.e., there exist a state j, such
that pj=1 and pi=0 for all i≠j, then the entropy of such rule table is
ER=0. When each possible state i appears in the rule table with the
same frequency, i.e. pi=1/k, then the entropy should get the
biggest value:
Si-1SiSi+1
000
001
010
011
100
101
110
111
k −1
k −1
1
1
1
E R = −∑ log k = −∑ (−1) = 1
k
i =0 k
i =0 k
That is to say, ER must be a real value between 0 and 1. In
addition, the greater ER is, the more chaotic the CA could be.
Si
0
1
1
0
1
1
1
0
Table 1 Rule table example regarding a 1-D 2-state Cellular
Automaton with neighbor radius of 2
As we can see, by using ER to measure the complexity of CAs, all
the possible states can be treated equally. For instance, a specific
Figure 1 The relationship between lambda and the Entropy of Rules in 2-states Cellular Automata
In the first place, we’d like to know how’s the difference between
these two measurement regarding the complexity of Cellular
Automata. Regarding 2-state Cellular Automata, the relationship
between lambda and the Entropy of Rules is very clear so that it
can be shown in a two dimensional graph as Figure 1. Since there
are only two states in the Cellular Automata, then there are only
two variables taken into account: p0 and p1 and they have to sum
up to 1. So it is easy to derive
λ=
ER = − p0 log p0 − (1 − p0 ) log(1 − p0 ) .
So it is obvious that lambda is a straight line in Figure 1 and the
more p0 is, the less lambda is. In this case, one can not say that the
Cellular Automaton is totally chaotic when lambda is 1 because
all the rules having the next state of 1 means that no matter the
initial states are, all the cells will turn into state 1 in just one step
and remain the same, which fulfills the definition of Wolfram’s
static category. So in this case, the totally chaotic category should
lie around p0=0.5. As we can see, the Entropy of Rules gets its
biggest value at p0=0.5 and decreases on both sides. So it is
reasonable to expect that Wolfram’s four categories lie on ER’s
axis in the exact order of static, cyclic, complex and chaotic. The
p1 = 1 − p0 . Then we have
N − N0
N
= 1 − 0 = 1 − p0
N
N
and
32
It is trivial to study the Cellular Automata with n=1, k=2 since
there are already many previous papers explored them. So they
are not included in the experiments in this paper. The first
experiment starts from n=2, k=2.
experimental results showing this phenomenon will be discussed
in the next part.
When the Cellular Automata have more than 2 states, the
relationship could be more complicated and can only be drawn in
a high dimensional space graphs, which are not shown here. But
the graphs depict a similar but not exact trend as in Figure 1.
3.1 Cellular Automata with two states and
neighbor radius of two
S AND RESULTS
3. EXPERIMENT
EXPERIMENTS
Since the neighbor radius is two, then each rule has to contain the
states of two neighbor cells on both sides and itself, or five cells’
states. And each cell can take one of two possible states. So the
rule table has 25=32 rules in total. Then since each rule may have
one of the two possible states as its next state, then there are 232
different rule tables or distinct Cellular Automata. So it is almost
not possible to enumerate all the rule tables and analyze them.
Fortunately, sampling them and statistically analyzing them is
sufficient for us to draw a qualitative conclusion. So in this
experiment, 250 samples have been drawn from the candidates
pool and classified as static, cyclic, complex or chaotic. The
lambda coefficient and the Entropy of Rules of each sample are
calculated as well.
To simplify the experiments and focus on the performance of
lambda and the Entropy of Rules, only one dimensional Cellular
Automata are considered, but with different neighbor radius n>0
and possible number of states k>1. The general idea of these
experiments are randomly generated different rule tables for one
dimensional Cellular Automata with fixed n and k. And then
calculate the lambda coefficient and the Entropy of Rules
respectively for each Cellular Automaton and classify them as
static, cyclic, complex or chaotic. Using these labeled Cellular
Automata as database, we can analyze the performance of lambda
and the Entropy of Rules statistically.
Figure 2 Distribution of Cellular Automata with different classes on lambda axis
The results are shown in Figure 2 and Figure 3.
Firstly, I’d like to know for each class (static, cyclic, complex or
chaotic), what’s the distribution of Cellular Automata on lambda
and the Entropy of Rules axis. To be more mathematically formal,
I’d like to know the possibilities of
The lambda distribution of static class in Figure 2 shows that
almost all of the static Cellular Automata lie on the both ends of
the lambda axis. This is rational and as mentioned before, almost
all the rules have the next state of 0 when the Cellular Automaton
has lambda close to 0, and almost all of the rules have the next
state of 1 if its lambda is close to 1. So these Cellular Automata
tend to be static. The distributions of cyclic and complex are very
similar, they both have two peaks in their own distributions. But
the peaks in cyclic distribution are closer to the two ends of
lambda axis than peaks in complex distribution are. And, from
Figure 2, it is almost impossible for a cyclic Cellular Automaton
to have the lambda around 0.5, which is possible for complex
Cellular Automata. In the chaotic distribution, there is just one
peak around 0.5 on the lambda axis. This is also easily
understandable since in 2-state case, if a Cellular Automaton has a
lambda coefficient around 0.5, then half of its rules have the next
Pr(λ ∈ X i , C )
,
Pr(C )
X i = (i / 10, (i + 1) / 10), i = 0,⋯ ,9,
Pr(λ ∈ X i | C ) =
C ∈ {static, cyclic, complex, chaotic}
and
Pr( ER ∈ X i | C ) =
Pr( ER ∈ X i , C )
.
Pr(C )
33
Figure 3 Distribution of Cellular Automata with different classes on ER axis
state of 1(or 0), and the 0 states and 1 states could appear in the
same frequency on any time step of the Cellular Automaton from
an arbitrary initial condition, so it is more likely to be chaotic than
the Cellular Automata with the lambda larger or smaller than 0.5.
Figure 4 Percentages of different classes in each of lambda’s intervals
Entropy of Rules is, the less order the Cellular Automaton has,
hence the more likely the Cellular Automaton is chaotic. As
shown in Figure 3, most static Cellular Automata have the ER
around 0.3 and 0.7 for most cyclic ones. Though both the peaks of
complex and chaotic classes are in the last column, the variance of
the distribution of complex class is obviously bigger than that of
chaotic class, which means a chaotic Cellular Automaton has
more possibility to have an ER bigger than 0.9 than a complex
Cellular Automaton does. If one subdivides the last column into
smaller intervals and draws a similar distribution, the peak of
Correspondingly, Figure 3 gives the Entropy of
Rules’
distributions of different classes. Intuitively, one may find that the
graph is more regular than Figure 2, because each of the four
categories has only one peak and the peaks of different classes lie
on the ER axis in the exact order of static, cyclic, complex and
chaotic. As we know, entropy is a description of order (or chaos)
originally. So the Entropy of Rules can be considered as a
description of how ordered or chaotic the rule table is, then even a
description of the order of the Cellular Automaton. The more the
34
chaotic class is expected to lie in the biggest interval as it is in
Figure 3, and the peak of complex class is likely to be a little
smaller than 1. The analysis has not been shown in this paper
since there may not be enough samples in the 0.9 to 1 interval to
conduct a convincing analysis. More analysis with more samples
is expected to be conducted in an extended work in the near future.
As we saw in Figure 2, a similar result regarding the lambda
coefficient can be found in Figure 4. In this graph, it is more clear
and formal that a Cellular Automaton from the first or the last
column is much more likely to be static than other classes. And if
a Cellular Automaton has the lambda around 0.5, then it is about
65% possible to be chaotic, and 30% possible to be complex.
Another conclusion can be drawn from Figure 5 is that the cyclic
and complex categories may appear in almost every interval in a
not low frequency. A similar result can also be found in Melanie
Mitchell et al.’s work[1].
In another point of view, how possible a Cellular Automaton in a
certain interval is static, cyclic, complex or chaotic also concerns
us. Again, in a formal mathematical form, we’d like to know:
Pr(C | λ ∈ X i ) =
Pr(λ ∈ X i , C )
,
Pr(λ ∈ X i )
Similarly, Figure 5 shows the possibilities of a Cellular
Automaton being static, cyclic, complex or chaotic given the
interval its ER belonging to. In the graph, we can see almost all the
Cellular Automata with ER lower than 0.7 are static, or cyclic. For
the Cellular Automata with ER bigger than 0.8, the possibility of
one of them to be complex or chaotic gradually increases along
with its ER. So the graph also support the saying mentioned before,
the peak frequencies of different categories happen on the ER axis
in the exact order of static, cyclic, complex and chaotic. However,
one may also noticed that on the ER axis, static and cyclic class
can happen in almost all the intervals. Again, I also argue that if
one subdivides the last interval into smaller ones, (s)he may find
that the fraction of static or cyclic drops sharply as the ER
increases.
X i = (i / 10, (i + 1) / 10), i = 0,⋯ ,9,
C ∈ {static, cyclic, complex, chaotic}
and
Pr(C | ER ∈ X i ) =
Pr( ER ∈ X i , C )
.
Pr( ER ∈ X i )
The first distribution regarding the lambda coefficient is shown in
Figure 4 while the other distribution about the Entropy of Rules is
drawn in Figure 5.
Figure 5 Percentages of different classes in each of ER’s intervals
So some part of the instance space has not been covered and the
result should be qualitatively instead of quantitatively valid. And
it will be shown that the neglected part of instance space is trivial
and does not impact the result.
3.2 Cellular Automata with three states and
neighbor radius of two
In the last experiment, both kinds of statistical graphs don’t
support the saying that Wolfram’s four categories generally lie on
the lambda axis in the order of static, cyclic, complex and chaotic.
But one may argue that this is an exception of 2-state Cellular
Automata. So in this section, an experiment on 3-state Cellular
Automata has been conducted. It is undoubtable that the instance
space is even much larger than that of last experiment. In this
experiment, 450 samples have been randomly drawn from the
instance space as the database. Even though more samples have
been drawn in this experiment than the last one, it may not suffice.
Firstly, similarly, we’d like to know how possible the lambda
coefficient or the Entropy of Rules of a Cellular Automaton lies in
each intervals given its classification:
Pr(λ ∈ X i , C )
,
Pr(C )
X i = (i / 10, (i + 1) / 10), i = 2,⋯ ,9,
Pr(λ ∈ X i | C ) =
35
and
Notice that the form is the same but the intervals are different.
Regarding the lambda coefficient, the first two intervals from the
first experiment are not covered in this experiment. But it doesn’t
effect the result since in the first two intervals, the lambdas of the
Cellular Automata are lower than 0.2, which means almost 80%
of the rules have the next state of 0. So most of these Cellular
Automata are static, hence it is not necessary to cover this part of
instance space. The result is shown in Figure 6.
Pr( ER ∈ Z i , C )
Pr(C )
Z i = (0,0.55)or (0.5 + 0.05i,0.55 + 0.05i ), i = 1,⋯ ,9
Pr( ER ∈ Z i | C ) =
C ∈ {static, cyclic, complex, chaotic}
Figure 6 Distribution of Cellular Automata with different classes on lambda axis
Figure 7 Distribution of Cellular Automata with different classes on ER axis
first interval is from 0 to 0.55. This is because when ER is lower
than 0.5, almost all of the Cellular Automata are static or cyclic
(mostly static), so it is not necessary to include them. Additionally,
by studying the definition of the Entropy of Rules, one may notice
that there is just a very small portion of the Cellular Automata
have ER lower than 0.5. So we can simply neglect them without
losing generality.
When lambda is lower than 0.8, the peaks of these four categories
lie on the lambda axis in the order of static, cyclic, complex and
chaotic. And the percentage of each interval for the chaotic class
increases as lambda goes up. However, when lambda is bigger
than 0.8, the percentage of chaotic class goes down when the
other classes have a little bit increment. We will come back to this
phenomenon later. In Figure 7, there is still only one peak for each
class, and the order of the peaks remains the same. Notice that the
36
What’s more, the possibilities of a Cellular Automata being static,
cyclic, complex or chaotic given a certain interval on lambda or
the Entropy of Rules’ axis are drawn in Figure 8 and Figure 9
respectively. It is more clear in Figure 8 that the peak of chaotic
class is not in the biggest interval but around 0.7. After 0.7, the
percentage of chaotic class decreases on the lambda axis. A
possible theory is, when the lambda increases, the less the rules
having the next state of 0 are. When the lambda coefficient equals
to 1, there is no rule having the next state of 0, then the 0 state
dies out on the second time step from any initial condition. So the
Cellular Automata lose part of freedom degree. Then they tend to
be more ordered when the lambda coefficient is big enough.
What’s more, one may also find in Figure 8 that the complex class
appears almost everywhere with a relatively high frequency. That
is to say, the lambda coefficient does not perform well in
distinguishing the complex category from other categories. In
Figure 9, it is shown that the bigger ER is, the more likely a
Cellular Automaton is complex, then chaotic and less likely to be
static or cyclic. So it is still consistent with the former claims
regarding the Entropy of Rules.
Figure 8 Percentages of different classes in each of lambda’s intervals
Figure 9 Percentages of different classes in each of ER’s intervals
In summary, no matter how many possible states the Cellular
Automata contain, the lambda coefficient is always not a good
description of the order of the Cellular Automata. The more
possible states the Cellular Automata have, the bigger variance the
distribution of the complex class could have. And the static and
cyclic classes could appear everywhere on the lambda axis.
What’s more, the peak of the distribution of the chaotic class is
always less than one, what happens between the peak and
lambda=1 is unpredictable. On the other hand, the Entropy of
Rules is always consistent with different kind of Cellular
Automata, meaning the four categories lie on the ER axis in the
exact order of static, cyclic, complex and chaotic no matter how
many possible states the Cellular Automata could have or how
37
wide the neighbor radius is. So in most of circumstances, the
Entropy of Rules outperforms Langton’s lambda coefficient.
because it better targets the complex category in its domain and
the complex category always concerns us much more than the
other three categories.
4. CONCLUSION
The work in this article can be extended in several different
aspects. First of all, to deal with the problem that the smaller part
of ER axis is too “empty”, a modified form originated from the
Entropy of Rules is expected to be introduced in a future work.
The problem can be solved by “left shifting” the center of ER
domain. Secondly, more specific experiments regarding the last
interval on the ER axis are expected to conduct. In this aspect,
more instance needs to be sampled from the largest ER part of the
instance space. Thirdly, more experiments are expected to conduct
on different kinds of Cellular Automata with more possible states
or/and wider neighborhood.
In this paper, Langton’s lambda coefficient has been reviewed and
several weaknesses of lambda in describing the complexity of
Cellular Automata have been found. To better describe the
complexity of Cellular Automata, a new measurement of
complexity, the Entropy of Rules (or ER), has been introduced in
this article. Theoretically, it is shown that some of lambda’s
weaknesses have been overcome by using this new measurement.
To experimentally prove such claim, several experiments have
been conducted. And the results show that, Wolfram’s four
categories didn’t lie on the lambda axis in the exact order as
claimed before. And regarding Cellular Automata with more than
2 states, each of Wolfram’s four categories could appear on the
lambda axis with nontrivial possibilities. On the other hand, the
Entropy of Rules performs consistently in all kinds of Cellular
Automata. To be more specific, Wolfram’s four categories lie on
ER‘s axis in the exact order of static, cyclic, complex and chaotic.
And the variances of the distributions of complex and chaotic
classes are much smaller than they are on the lambda axis.
5. REFERENCES
[1] Melanie Mitchell, James P. Crutchfield, and Peter T. Hraber.
1994. Dynamics, Computation, and the “Edge of Chaos”: A
Re-Examination. Complexity: Metaphors, Models, and
Reality.
[2] Francois Blanchard, Petr Kurka, and Alejandro Maass. 1997.
Topological and measure-theoretic properties of onedimensional cellular automata. Physica D: Nonlinear
Phenomena. 103, 1-4(Apr. 1997), 86-99. DOI=
http://dx.doi.org/10.1016/S0167-2789(96)00254-0
However, the Entropy of Rules also has some weaknesses. As we
can see in the Figures, most of the complex or chaotic Cellular
Automata lie on a small portion on the right of the ER axis and the
static and cyclic classes occupy most part of the axis. This may
because just a very small portion of the Cellular Automata have
low ER and a small range of ER on the biggest end of the axis
contains most of the Cellular Automata. What’s more, it is not
easy to distinguish static and cyclic class from the ER axis,
meaning the distribution of these two categories hugely overlap
with each other. So either the lambda coefficient or the Entropy of
Rules has its own advantages. But as far as I’m concerned, the
Entropy of Rules is better than Langton’s lambda coefficient
[3] C. E. Shannon. 2001. A Mathematical Theory of
Communication. The bell system Technical Journal, Vol.
XXVII, No. 3.
[4] Chris G. Langton. 1990. Computation at the edge of chaos:
Phase transitions and emergent computation. Physica D:
Nonlinear Phenomena. 42, 1-3(Jun. 1990), 12-37. DOI=
http://dx.doi.org/10.1016/0167-2789(90)90064-V
38
ASOP- Adaptive Self-Organizing Protocol
John Edison
University of Central Florida
Department of EECS
JEdison@knights.ucf.edu
Abstract
In this paper we wish to explore the various
energy efficient protocols in wireless sensor
networks. There has been must research done on
extending the battery life, however most
protocols require some sort of centralized
clustering phase. In this paper we propose a self
organizing protocol that can also adapt over time.
If every sensor did not have to transmit to the
sink for clustering, energy costs can be reduced.
Keywords
Wireless Sensor Networks, LEACH, HEED,
ADRP, CSMA, CDMA, TDMA, IEEE 802.11,
Agent Based Modeling, NetLogo, Complex
Adaptive Systems, Self-Organization, Clustering,
Energy Efficient MAC Protocols
1.
Introduction
1.1
Wireless Sensor Networks
Figure1: Example of wireless sensor network [7]
energy drain. This works because the cluster
head will relay the data from a sensor to the sink.
Cluster heads will be rotated based on criteria set
by each of the specific protocols.
Wireless sensors networks are a more recent
popular technology. These networks consist of a
population of homogeneous sensors. Figure 1
gives an example of a wireless sensor network
with an adhoc protocol. In this paper we do not
wish to explore the adhoc structure shown in
Figure 1 because it would not allow for sensors to
go into sleep mode. The job of these sensors is to
monitor its surroundings for a specific event to
trigger and then to wirelessely transmit data to a
sink. A major issue with these networks is that
the sensors are battery powered and are often
deployed in areas where the batteries can not be
changed easily. There has been much research
done on how to conserve energy by keeping the
sensors in sleep mode as much as possible. One
proposed solution is clustering the sensors into
subnetworks and only keep one cluster head in
each subnetwork awake to take most of the
2.
Model
2.1
Agent Based Modeling
Agent based modeling is a powerful tool for
simulating the behavior of complex adaptive
systems. The models try to explain the global
behavior of a system that the parts or agents of a
system can not explain. Because a wireless
sensor network consists of a population of
homogeneous sensors, agent based modeling can
be a powerful tool to simulate and test new
protocols.
2.2
Architecture
For this research project I will be using Netlogo
5.0.2 multi-agent environment. Netlogo provides
an easy and great environment for agent based
modeling and simulation.
For the power
calculations in this experiment I have chosen to
use the classical model paired with the free-space
39
path loss for power calculations.
I had
considered using the micro-amps model however
these calculations do not include distance in the
power equations so clustering would show no
boost in performance. Shown below are the
constant values for the classical model as well as
the free-space path loss equations I used.
include the random cluster head rotation,
centralized initial clustering, and fixed initial
clustering configuration.
3.2
HEED
Hybrid Energy Efficient Distributed Clustering
(HEED) was an extension of LEACH. This
protocol is similar to LEACH in that it has
centralized initial clustering. It also uses the
TDMA for intra-cluster communication and
CDMA for inter-cluster communication. The
major improvement HEED has over LEACH is
that cluster heads are rotated based on their
current energy level. Like LEACH this protocol
has fixed initial clustering configuration.
Figure 2: Classical model constant values [6]
3.3
ADRP
Adaptive Decentralized Reclustering Protocol
(ADRP) came around as an extension to HEED.
It shares the initial clustering technique that
LEACH and HEED use. It also shares the
clustering rotation based on current energy level
like HEED uses. The major improvement this
protocol introduced was an adaptive reclustering
technique. The major problem with this protocol
is that it's deceiving in that it is not decentralized.
Every so often the network will transmit data to
the sink for reclustering. This protocol does not
make much sense but has been accepted as an
improvement.
Figure 3: Free-space path loss equations [6]
In the equations shown in Figure 3 k represents
the number of bits that will be transmitted and r is
the distance that the sensor will need to amplify
its signal by in order to reach its destination.
3.
Energy Efficient Protocols
3.1
LEACH
Low Energy Adaptive Clustering Hierarchy
(LEACH) was the first of the energy efficient
clustering techniques proposed.
The sensor
network has an initial startup clustering phase
where every sensor transmits its current location
to the sink. A Clustering algorithm is run and
subnetworks are formed and cluster head
assignment is done so that the network can be
live. Sensors are given a TDMA time slot for
intra-cluster communication and every cluster
head
uses
CDMA
for
inter-cluster
communication or communication to the sink.
Cluster heads are rotated randomly after each
transmission. Major issues with this protocol
3.4
ASOP
Adaptive Self-Organizing Protocol (ASOP) is a
true implementation of ADRP. It not only
implements decentralized reclustering but also
self-organizes and continuously adapts over time
to maximize clustering efficiency. This protocol
uses many concepts found in various wireless
protocols as well as those specific to wireless
sensor networks.
The way ASOP self organizes is similar to how
IEEE 802.11 works. A sensor that is not
currently assigned to a cluster head will broadcast
40
Figure 4: Initial configuration of sensors with
population of 400
Figure 5: Sensor network at time step 1841 with
population of 500
a request to send (RTS) packet. The sensor will
use CSMA similar to the one used in 802.11 to
try and avoid collisions at all costs. If a cluster
head is in range and has not reached the cluster's
capacity then it will receive a clear to send (CTS)
packet that will also include a TDMA scheduling
slot. If no CTS packet is received then the sensor
assumes responsibility as cluster head and a new
cluster is formed. Since every cluster head will
know about neighboring cluster heads in the
network, occasionally a cluster head will trigger a
handoff for a sensor to a join a different cluster.
origin. Every sensor will transmit following a
Poisson distribution because this has been widely
accepted as typical network conditions in queuing
models. For each deployment all four protocols
will be run on that exact configuration to ensure
fair and accurate results. The sensors will be
deployed and redeployed for a total of ten times
per simulation and the runs will be averaged out
in the graphs shown in the data and results
section.
4.
Experiment
4.1
Simulation configuration
4.2
Simulation with 400 sensors
In this simulation 400 sensors were normally
distributed as shown in Figure 4. The red circles
in Figure 4 represent cluster heads and the yellow
circles in Figure 4 are the regular sensors
assigned to the closest cluster head.
This
simulation consisted of a less dense population
than the other two. Each sensor could be a
maximum of 10 cells away from their associated
cluster head.
Each cluster could have a
maximum of 17 sensors before a self-breathing
mechanism would create a new cluster and
cluster head.
For my experiment I will run two different
simulations. Both simulations will be run in a
100x100 grid with a normally distributed sensor
deployment. Each sensor will take up one cell
and may or may not move around depending on
the simulation. The initial energy level of each
sensor will be one million pico joules. In both
simulations the sink will be placed in the center
of the grid which will also be considered the
41
4.3
Simulation with 500 sensors
In this simulation 500 sensors were normally
distributed as shown in Figure 5. The red circles
in Figure 5 represent cluster heads, the yellow
circles Figure 5 are the regular sensors assigned
to the closest cluster head, the black triangles in
Figure 5 are sensors that died as a cluster head,
and finally the black circles in Figure 5 are the
sensors that died as normal sensors. Like in the
previous simulation, each sensor could be a
maximum of 10 cells away from their associated
cluster head.
Each cluster could have a
maximum of 17 sensors before a self-breathing
mechanism would create a new cluster and
cluster head. The major difference in this
experiment is that a second run was also
performed where the sensors would be mobile.
Sensors would move around randomly with a
probability of 0.0006.
5.
Data and Results
5.1
Simulation with 400 sensors
5.2
Tables 2 and 3 as well as Figures 7 and 8 show
the outcome of these simulations. In the nonmobile simulation ADRP was again found to
have the worst performance due to the cost of
reclustering periodically. HEED and LEACH
have about the same performance. Table 2 shows
that ASOP is seen to perform the best overall
because of its ability to adapt over time.
500 non-mobile
LEACH
HEED
100 (sensors dead)
534 (time step)
200
712
300
879
400
1164
500
3741
LEACH
579 (time step)
786
1113
5279
HEED
624
801
1106
4537
ADRP
604
745
979
3984
ADRP
640
711
845
1103
2423
ASOP
556
628
749
1070
2895
686
823
989
1281
6681
Table 2: 500 non-mobile simulation results
In the mobile simulation HEED, LEACH, and
ADRP are all seen to perform about the same. I
think ADRP became more practical for this
simulation because the sensors were moving
around and adaptation would be more useful.
However, the cost of reclustering did not
outweigh the boost in performance. Like in the
previous simulations, Table 3 shows that ASOP
performs the best overall.
Table1 and Figure 6 show the outcome of this
simulation. ADRP was found to have the worst
performance due to the energy cost of reclustering
periodically. HEED barely outperforms LEACH
because it extends the total life of the network
longer than LEACH does. Finally ASOP is seen
to perform the best overall because of its ability
to adapt over time and not require the overhead of
transmitting to the sink to do so. ASOP is seen to
have a heavy advantage of the other protocols as
shown in Table 1.
400 non-mobile
100 (sensors dead)
200
300
400
Simulation with 500 sensors
500 mobile
LEACH
HEED
100 (sensors dead)
613 (time step)
200
697
300
867
400
1095
500
2230
ADRP
604
698
802
1118
2423
ASOP
606
754
822
1185
2369
Table 3: 500 mobile simulation results
ASOP
700
895
1295
8498
Table 1: 400 non-mobile simulation results
42
679
794
954
1340
6598
Run with 400 sensors
450
400
Number of dead sensors
350
300
250
LEACH
HEED
200
ADRP
ASOP
150
100
50
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Time step
500
500
400
400
300
300
LEACH
200
ADRP
200
100
100
0
0
0
1000
2000
3000
4000
0
5000
500
500
400
400
300
1000 2000 3000 4000 5000
300
HEED
200
ASOP
200
100
100
0
0
1000
2000
3000
4000
0
5000
0
2000
4000
6000
8000 10000
Figure 6: Graphs tracking the number of dead sensors for the non-mobile run with 400 sensors. All
axis have the same labels but were removed from the individual run graphs for readability.
43
Run with 500 sensors
600
Number of dead sensors
500
400
LEACH
300
HEED
ADRP
ASOP
200
100
0
0
1000
2000
3000
4000
5000
6000
Time step
600
600
500
500
400
400
300
300
LEACH
200
200
100
100
0
0
0
1000
2000
3000
ADRP
0
4000
500 1000 1500 2000 2500 3000
600
500
600
400
500
400
300
HEED
200
300
100
200
0
100
0
500 1000 1500 2000 2500 3000
ASOP
0
0
1000 2000 3000 4000 5000 6000
Figure 7: Graphs tracking the number of dead sensors for the non-mobile run with 500 sensors. All
axis have the same labels but were removed from the individual run graphs for readability.
44
Run with 500 mobile sensors
600
Number of dead sensors
500
400
LEACH
300
HEED
ADRP
ASOP
200
100
0
0
1000
2000
3000
4000
5000
6000
7000
Time step
600
600
500
500
400
400
300
300
LEACH
200
200
100
100
0
0
0
ADRP
0
500 1000 1500 2000 2500
600
600
500
500
400
400
300
500
1000 1500 2000 2500
300
HEED
200
200
100
100
0
ASOP
0
0
1000 2000 3000 4000 5000
0
2000
4000
6000
8000
Figure 8: Graphs tracking the number of dead sensors for the mobile run with 500 sensors. All axis
have the same labels but were removed from the individual run graphs for readability.
45
6.
[2] B Baranidharan, B Shanthi. A New Graph
Theory based Routing Protocol for
Wireless Sensor
Networks.
International Journal, 2012 – airccse.org
Conclusion
LEACH and HEED had the predicted results,
however ADRP performed differently than
expected. There are many claims that ADRP
would outperform LEACH and HEED but the
overhead in reclustering outweighed the benefit.
ADRP only competed competitively against
LEACH and HEED in the 500 mobile simulation
because it's adaptation would have more effect on
performance. In all of my simulations I found
ASOP to outperform the other protocols. The key
advantage ASOP has over the other traditional
protocols is that it can self-organize and adapt
over time.
7.
[3] B. Baranidharan and B. Shanthi. An Energy
Efficient Clustering Protocol Using
Minimum Spanning Tree for Wireless
Sensor Networks. PDCTA 2011, CCIS 203, pp.
1–11, 2011.
[4] A Garcia-Fornes, J H¨ ubner, A Omicini, J
Rodriguez-Aguilar, V Botti. Infrastructures and
tools for multiagent systems for the new
generation of distributed systems. Engineering
Applications of Artificial Intelligence 24 (2011)
1095–1097
Extensions
ASOP was able to outperform the other energy
efficient MAC protocols in this experiment,
however it can still be greatly improved. In all of
my simulations there was only single hop routing.
I am pretty sure performance would be greatly
improved if my protocol could be paired with an
energy efficient multi-hop routing protocol.
Another extension that might be interesting
would be to run simulations on more mobile
sensor networks. I would think that because
ASOP is adaptive over time it will have an even
greater advantage with a more mobile sensor
network than the more static deployments.
8.
[5] L Mottola, G Picco. Programming Wireless
Sensor Networks: Fundamental Concepts
and State of the Art. ACM Computing
Surveys, Vol. 43, No. 3, Article 19, Publication
date: April 2011
[6] M Torres. Energy Consumption In Wireless
Sensor Networks Using GSP. Thesis.
References
[7]
Alico.
Sensor
Network
http://www.alicosystems.com/wireless
%20sensor.htm
[1] F Bajaber, I Awan. Adaptive decentralized reclustering protocol for wireless sensor networks.
Journal of Computer and System Sciences 77
(2011) 282–292
46
Image.
Agent Based Model for Leftover Ladies in Urban China
Jun Ding
Department of EECS, University of Central, Orlando , FL, 32816 ,USA
ABSTRACT
Leftover ladies phenomenon is a serious problem in China and some other Asian countries.
Lots of women cannot get married after their 30s and some of them cannot even get married
anymore. This problem has a great impact on China’s society. Lots of researches have
been done regarding to this topic. However, all of them are qualitative. In this paper, we
have proposed an agent-based model to study this problem quantitatively. The model
proposed in this paper is the first quantitative model to study and analyze the “leftover
ladies” phenomenon. Therefore this study provides a tool for researchers to study this
problem quantitatively and thus it is very helpful.
INTRODUCTION
In the recent decades, leftover ladies (or shengnv) phenomenon are getting more and more
attention by the public media, and even social science researchers. Although the word of
"leftover ladies" are very popular, its definition is somehow unclear. Normally, women who
remain single after their 28 or 30 are regarded as "leftover ladies". Those "leftover ladies"
are always tagged as 3S, Single, Seventies (Most of them were born in 1970s), Stuck.
In China, heterosexual marriage has long been the prerequisite for the family formation and
continuity. Along with the childbirth, it is the central marker of adulthood; Family in turn is an
important arena of gender socialization and identity marking. For much of Chinese history,
women’s identity, role and status derived from her kinship position and membership in a
kinship group (Barlow 1994). Today, femininity is still associated with those characteristics
befitting a "traditional", "virtuous wife and good mother", although women's social status may
depend more on the conjugal relationship than ever before. As a social and economic entity,
the family units is the building block for the modern nation-state, as the producer of citizenry
and the labour. Symbolically, a harmonious family begets harmonious society and a stable
polity. Given the paramount significance of family historically and culturally in China, it is no
wonder that shifts in marriage patterns garner extensive attention and cause consternation.
Thus, although the state encourages late marriage as part of its effort to limit family size, the
specter of large cohorts of unmarried singles raises alarm. Indeed, when releasing the
recent data on unwed singles, the Shanghai Municipal Statistic Bureau warned: "problems
with relationships or marriage not only affect citizen's work, study or life, but also bring about
uncertainty to society as a whole" (Cao 2007).
47
Some researchers predicted in 1997: With the development of society, the "leftover ladies"
will increase rapidly. Now, this prediction get validated. According to the data from 2005 "
Chinese society comprehensive study", 1997-2005, the rate of unmarried women age 30-34
increases from 1.2% to 3.4%. This data indicates the "leftover ladies" phenomenon are
becoming serious. Besides, the data also shows that these "leftover ladies" are mainly from
the urban areas, especially the largest cities, such as Beijing, Shanghai, Honkong and etc.
In 2005, there are more than 300,000 "leftover ladies" in Beijing, 430,000 "leftover ladies" in
Shanghai. These figures keep increasing in the last few years. Until 2009, the number of
"leftover ladies" in Beijing is larger than 800,000. Since this phenomenon is becoming a
serious problem for the whole society, lots of researches were performed to analyze and
understand it.
In paper (Gaetano 2007), the authors explain the reason for the “leftover ladies”.
The
reasons were classified into two types: (1) External, which means the reasons related to
external factors, like economy, religion and etc. (2) Internal, which means the reasons
related to internal factors, wealth, education, age, appearance, and etc. In another study
(Zuo 2011), the authors also take the internal factors, such as wealth, education, age,
appearances and etc as the important reasons for the leftover ladies phenomenon.
Therefore, in this study, our model was constructed based on 4 main internal factors, wealth,
education, age and appearances.
METHODS
In this part, we will build our agent-based model for "leftover ladies" based on the 4 virtues
mentioned in the previous studies: appearance, wealth, education, and age. These 4 virtues
were regarded as critical factors for women to choose their husbands.
1. Agents
There are two types of agents will be used in the agent-based model. They are men agents
and women agents. The following figure demonstrates the features of men and women
agents.
48
age
age
wealth
wealth
score
children
Men
education
Women
appearance
education
appearance
score
attractivenes
s
Figure 1 Features of Agents
2. Agent Rules
For all agents in the model, they all follow the rules described as below.
(1) Wiggle-Waggle
If An agent, men or women, is still single, it will move around the "world". This can give
change to each man/woman agent to meet another woman/man. Once an agent
get
married, then it will become stable, since there is no need for him/her to meet somebody
else for marriage. (In this model, we don't take the divorce into consideration.)
(2) Date
A woman agent will randomly choose a man of marry-age out of her attractiveness range as
her date. The marry-age here means the minimal age for marriage required by the Law. The
attractiveness range shows the extent of the charm of women agent. The larger
attractiveness means she can attract men within larger range, see figure 2.
Attractiveness
Man attracted
Man not attracted
Woman
Figure 2 Attractiveness of Woman
49
Attractiveness is a function of features of women agent. In this model, the attractiveness of a
woman agent is defined as follows:
wealth
* wealth _ weight _ women _ attractiveness
10
education

* education_ weight _ women _ attractiveness
4
appearance

* appearance_ weight _ women _ attractiveness
10
abs( age  20)
 (1 
) * age _ weight _ women _ attractiveness]
60
Attractiveness  10 * [
Where,
wealth  [0,10]
education [0,4]
appearance [0,10]
w
age  [20,80]
wealth _ weight _ women _ attractiveness  education_ weight _ women _ attractiveness
 appearance_ weight _ women _ attractiveness  age _ weight _ women _ attractiveness  1
wealth_weight_women_attractiveness
denotes
attractiveness.
the
weight
of
wealth
on
women
beducation_weight_women_attractiveness,
appearance_weight_women_attractiveness and age_women_attractiveness were defined
similarly. The sum of all the weights equals to 1 and the attractiveness ranges from 0 to 10.
(3) score
The women agents score her date based on a function of the 4 features used in the model,
wealth, education, appearance, and age. The scoring function can be written in the following
format:
wealth
* wealth _ weight _ men 
10
education
* education _ weight _ men 
4
abs( age _ 20)
[1 
] * age _ weight _ men＋
60
appearance
* wealth _ weight _ men
10
score 
wealth _ weight  education_ weight  age _ weight  appearance_ weight  1
50
The score defined above is normalized and therefore score ranges from 0 to 1.
(4) marry
The women agents score themselves and then decide whether to marry their date based on
the comparison of score_herself and score_date.
if score _date   pickness * score _ herself
 marry the date
else
 reject the date
score _ herself 
wealth
* wealth _ weight _ women 
10
education
* education _ weight _ women 
4
abs(age _ 20)
[1 
] * age _ weight _ women＋
60
appearance
* wealth _ weight _ women
10
Similarly, the above score is also normalized and thus it ranges from 0 to 1. The above
marry decision demonstrate that if the men is above the pickiness level of the women agent,
she will marry her date, otherwise, she will reject. Traditionally, the women always want to
marry the men, who are better than herself. That means, the pickiness level is usually larger
than 1.
(5) Reproduction
If a married woman, whose children number is smaller than the limit required by the Law.
Then, this woman has a change to give birth to a new agent.
married women :
if # of children  lim it
chance  birth _ rate of the society
she has a chance to give birth to a new agent
The wealth, education, and appearance distribution of new born agents is the same as the
distribution of the original agents. The age of new born agents are all 0.
(6) Age and die
51
Each tick, the age of each agent increases by 1.
if agent age  die _ age (80 in this mod el )
 agent die
each tick
age  
RESULTS
1. Simulation setup
The simulation setup, the initial population were set as 200 men and 200 women. The wealth,
education, and appearance of agents are normally distributed. The age of agents are
randomly distributed. See the following initial setup figure.
Figure 3 Initial simulation setup
2. Results
(1) “Leftover ladies” phenomenon was observed in the simulation
The “leftover ladies” phenomenon was observed in our simulation. In the simulation result
given below, we can easily find out that there are certain percentage of women cannot marry
after their 30 (Leftover ladies definition used in the model), those women were regarded as
“leftover ladies”.
52
Figure 4 Leftover ladies phenomenon
(2) Pickiness level has a great impact on “leftover ladies” phenomenon.
We have tried two sets of simulations with two different pickiness level, 1 and 2. The other
initial setups for these two simulations are exactly the same. From the simulation results
shown below, the importance of pickiness level can be readily found.
a. Pickiness level=2
Figure 5 Simulation Result (Pickiness=2)
b. Pickiness level=1
53
Figure 6 Simulation Result (Pickiness=1)
When we reduce the pickiness level from 2 to 1, the percentage of “leftover ladies”
decreases dramatically. This supports that the pickiness is an important factor to “leftover
ladies” phenomenon. The reason is very straightforward. If the pickiness level is high, that
means all the women agents in the model tend to be harder to marry her date. Then, there
will be more women cannot marry after their 30s and therefore become “leftover”.
(3) Mate choice is an important factor for “leftover ladies” phenomenon.
Even in the same pickiness level, different Mate choice, which means different weights on
different features (wealth, education, appearance, etc. ), also affect the “leftover”. There are
two types of mate choice in this model: Men choose Women, Women choose Men. The
former was modeled as women’s attractiveness; the men tend to choose women with larger
attractiveness. The later was modeled as the comparison between the scores of women and
her date. If we set the weights for attractiveness or score differently, that means the agents
(both women and men) valued different features. For example, if we set large weight for
wealth for attractiveness, which means wealth, women are more attractive for the men. By
simulating on different sets of weights, we have found that the mate choice is also a very
important factor for “leftover”.
a. Men valued the appearance of women matters, as well as others. Women valued similarly.
54
Figure 7 Simulation Result (mate choice a)
b. Men only valued the wealth, while women only score themselves based on their
appearance.
Figure 8 Simulation Result (mate choice b)
In the above two simulations, (b) have larger percentage of “leftover”, compared with (a).
This illustrates that the mate choice is really an important factor for “leftover ladies”. To
55
explain the simulation result, we need take the mate choice difference into consideration. In
(a), how the men valued the women is somehow similar with how the women valued
themselves. However, in (b), the men only valued the wealth, while the women only valued
the appearance. This mate choice difference makes the women cannot attract the men she
want to marry and therefore lots of women becomes “leftover”.
(4) Leftover ladies tend to be high educated, wealth.
In our simulation, we also try to analyze the social status for those “leftover ladies”. Their
education level and wealth were also analyzed in the simulation, as shown in the figure
below.
Figure 9 Simulation Result (Education and Wealth level of leftovers)
In the above simulation result, the average level of education and wealth of “leftover ladies”
(red line) is higher than those married women. This can be explained as the high educated
and wealth women tend to be pickier and therefore they have larger chance to be “leftover”.
DISCUSSION
Based on the above simulations and analysis, we may try the following method to solve the
“leftover” ladies problem. First, we can use the public media to help to reduce the pickiness
level. For example, we can use the TV show or broadcast to generate the social pressure.
Therefore, these potential “leftover” ladies may lower their pickiness level. Second, we can
also help all the people to form the correct principle of mate choice and thus it is easier for
them to find and marry the date. Eventually, the “leftover ladies” problem can be relieved.
56
REFERENCES
[1] Arianne Gaetano, 2009. “Single Women in Urban China and the unmarried crisis:
Gender
resilience and Gender Transformation” , 2009 Working paper Nov.31
[2] Barlow, Tani. 1994. "Theorizing Woman: Funu, Guojia, Jiating" (Chinese woman,
Chinese state, Chinese family). In Body, Subject, Power in China.Ed. Angela Zito
and Tani E. Barlow, 253-289. Chicago: University of Chicago Press.
[3] Cao Li. 2007. "Single women on the rise in Shanghai." Chinadaily.com.cn,13
February.
(http://en.bcnq.com/china/2007-02/13/content_807828.htm...) Accessed 9 July 2008.
[4] Zuo X, Song XD, and et.al, 2011. “Exploration of the approach to plight the matrimony of
modern leftover women”
Journal of Shandong Youth University of Political Science.
57
Wealth Redistribution in Sugarscape:
Taxation vs Generosity
Vera A. Kazakova
Department of EECS
University of Central Florida
Orlando, Florida 32816
rusky.cs@gmail.com
Justin Pugh
Department of EECS
University of Central Florida
Orlando, Florida 32816
x4roth@gmail.com
ABSTRACT
Thus our question in conducting this research is not about
the necessity of wealth redistribution itself, but about the
best approach for such reallocation of resources. Many believe that our tax system is unfair toward those that have
to pay taxes to support the unemployed, for example. This
group may feel that ”freeloaders” emerge in society (consequently lowering productivity) precisely because these taxbased safety-nets exist, and thus may feel that relying on
voluntary donations to subjectively-legitimate organizations
would be a more sensible approach to helping those in need.
We present two extensions to the Sugarscape model designed to study the effects of two distinct methods of wealth
redistribution (taxation and generosity) under two socioeconomic climates: peaceful and prosperous vs strained by
scarcity and violence. Systematic experiments reveal relationships between the rates of tax or generosity and the
population-level statistics such as the Gini Coefficient, death
rates, productivity, and average wealth. Furthermore, the
two methods of wealth redistribution are shown to both successfully reduce the wealth disparity across the population,
although each method showcased noticeably different benefits and side-effects. This paper establishes that while taxation is a highly controllable and thus more reliable way
to shape an economy, generosity is also a powerful tool for
wealth redistribution, and possesses several observed advantages over a taxation-driven approach.
On the other hand, some believe that our economic system (capitalism) is highly conducive to disparities in wealth
among the population, and that it is neither ”fair” nor most
efficient in terms of bettering society as a whole. This group
may feel that voluntary donations would be insufficient to
fairly reallocate resources and thus believe a more forceful
redistribution of wealth is in order (i.e. taxation). This
method of wealth redistribution clearly encompasses a lot
more than helping the unemployed, as governments have
customarily used it to provided services such as, for example,
police departments. It could be argued that the availability
of such services would become unreliable if they were to be
sustained by voluntary donations only. As a result, a compromise between the two redistribution methods appears to
be the more sensible solution.
Categories and Subject Descriptors
K.4.m [Computers and Society]: Public Policy Issues
General Terms
Design, Experimentation, Economics
Keywords
Clearly the choice of how best to redistribute wealth is a
difficult one, and we do not claim to provide an irrefutable
answer. However, we do feel that our model provides some
insight into the strengths and weaknesses of each of these two
approaches, and future extensions might eventually inspire
a promising third option.
Sugarscape, Netlogo, Taxation, Altruism, Generosity, Economic Model
1.
INTRODUCTION
It is clear that in today’s society many people disagree over
how best to redistribute wealth to better the society as a
whole. We are of the mind that wealth redistribution is ultimately necessary (regardless of the way it is achieved),
as every individual should have access to basic comforts
such as food and shelter, and also to basic avenues for selfimprovement such as education and medical care.
The goal of this paper is to observe the effects of wealth redistribution in a society whose survival is dependent on said
redistribution (i.e. a gatherer/warrior model where gatherers cannot fight against threats, and warriors cannot gather
food). Specifically we analyze the effects of two different
wealth redistribution paradigms: voluntary (i.e. donations)
vs. mandatory (i.e. taxes). Our research allows us to give
some preliminary answers to questions such as: in a population without any outside threats, how do increases in
taxation or generosity affect the wealth distribution, productivity, or death rates? How do these effects differ when
a society has to deal with explicitly free-loading warriors
(who cannot gather food, but who protect gatherers from
enemies)?
58
In the following sections we will go over the inspiration and
basis for our experiments, i.e. Epstein and Axtell’s Sugarscape [5] (section 2), as well as the reasons for our proposed changes and the details behind the Taxation-based
and Generosity-based Sugarscape models (section 3). We
will then conduct a series of tests on Epstein’s Sugarscape
model with a few tweaks in order to establish a baseline for
comparison (section 4.2). In section 4.3 we will extend this
base model by implementing taxation and altruism individually, and analyze the results. In section 4.4 we incorporate enemies and warriors into our domain, and once again
test all three models (No-Taxation-No-Generosity, TaxationOnly, and Generosity-Only) on the newly modified Sugarscape. Discussion, conclusions, and future work can be
found in sections 5, 6, and 7, respectively.
2.
ditional Sugarscape are called Gatherers in this paper. For
a more detailed description of Sugarscape, refer to [5].
BACKGROUND
Humans are often believed to be self-serving, and the motives behind any observed altruism between members of a
society can be easily called into question: perhaps the act
of helping another human being is performed in order to
achieve some egocentric goal, such as the pursuit of positive
reputation, or a desire to make friends who might be useful
later, or whose presence will provide us with a higher social
status. Some argue that culture is responsible for generous behaviors observed in humans, rather than genetics [3].
However, the evolution of cooperation among self-interested
agents has been thoroughly explored in the literature [1, 6,
4, 2]; the consensus is that altruism can indeed emerge in
an evolutionary setting among purely self-interested agents,
and at least in the case of humanity and several species of
primates, it has. This means that humans have a genetically coded predisposition towards generosity that exists
manifests itself regardless of culture. Instead, culture can
either nurture of suppress this innate inclination towards
Generosity, a dynamic succinctly described by Francis Galton as “Nature vs Nurture”. This paper seeks to identify the
positive and negative aspects of Generosity as a method of
wealth redistribution and to compare it to and contrast it
with a Tax-based approach.
Figure 1: A visual display of the Sugarscape landscape. Darker regions contain more sugar, with the
darkest regions containing 4 sugar and the lightest
regions containing 0 sugar. Gatherer agents are depicted as small dots, Warrior agents (described in
section 3.3) are depicted as pentagons, and Enemies (described in section 3.3) are depicted as ghosts
(bottom left corner).
3.
DOMAIN: EXTENDED SUGARSCAPE
We propose to re-distribute the sugar-wealth of a typical
Sugarscape population through either a system of mandatory Taxation, a system reliant on voluntary donations, or
a sensible combination of the two.
This paper is largely an extension of the basic Sugarscape
model, originally presented by Epstein and Axtell. Epstein
and Axtell constructed the Sugarscape model as a means of
studying social behaviors in humans such as trade, group
formation, combat, and the spread of disease [5]. The world
of Sugarscape consists of a two-dimensional grid. On each
grid space grows a predetermined amount of sugar, a precious resource that the agents within Sugarscape depend
on for survival. A visual display of the typical Sugarscape
landscape populated with agents of various types is shown
in figure 1. On each tick of Sugarscape simulation, sugar
regrows on each space at a constant rate up to the maximum amount of sugar allowed for the space. One at a time,
agents move to the location with the highest sugar within
their field of vision, gather all of the sugar at that location,
and then consume sugar from their personal store equal to
their metabolic rate. Agents are heterogeneous across several attributes selected randomly at birth: metabolic rate,
vision radius, initual sugar holding, and maximum lifespan.
An agent who runs out of sugar or whose age exceeds their
lifespan dies and is replaced by a new agent with different
randomly selected attributes. The agents described by tra-
3.1
Taxation-Based Wealth
Redistribution Model
Our first method for redistributing the total sugar-holdings
within the population is through compulsory tax payments.
These will be collected from each Gatherer once per tick, and
will correspond to an externally set percentage of the sugar
a Gatherer collects during the time step. While the amounts
will differ based on actual sugar collected on that tick, the
percentage itself will remain the same for all Gatherers for
the entire duration of a given simulation. This percentage,
representing the proportion of sugar income that is to be
paid as taxes, will be systematically varied and analyzed
in sections 4.3 and 4.4, corresponding to our experiments
with and without Warriors and Enemies (explained in section 3.3), respectively.
Under the forced wealth redistribution paradigm, all gathered food is taxed at a fixed rate (determined by a parameter
setting) and spread out evenly amongst the poorest members of society. The taxed sugar will be given out to the least
wealthy members of the population, such that the wealth of
59
the poorest individuals is equalized. This method can be
easily understood through an analogy. Imagine a staircase
with water flooding it starting from the base. As the water
level rises and reaches the first step of the staircase, the base
of the stairs and the first step become equalized. As the water continues to rise, more and more steps are submerged
and thus their heights become equalized by the water level.
The rising water represents the collected taxes, with which
we “flood” the sugar-holdings of the individuals with least
wealth (represented by the bottom steps). We keep spreading the wealth until we run out of collected taxes (water
stops rising, but all the steps below water level are now of
equal height). If you find the idea of water as an equalizer
of height confusing, you may instead imagine the staircase
is being flooded by a rising level of concrete.
3.2
environment, and Enemies, who attack both Warriors and
Gatherers alike. Hence forth this model will be called the
Warrior-Enemy Sugarscape. It should be noted that Enemy
turtles are not considered to be a part of our society, and
are instead to be regarded as a characteristic of the simulation environment where our Warrior and Gatherer turtles
reside, i.e. Enemies do not gather or consume food, they
are spawned at a random location at a predefined constant
rate, and their deaths are not reported as part of our society’s death rates.
Generosity-Based Wealth
Redistribution Model
Our second method for redistributing the total sugar-holdings
within the population is through voluntary donations. These
are made according to an individual’s propensity to donate,
and thus will vary across the population. Generosity-based
behaviors have also been referred to as Altruism in related
literature; throughout this paper, however, we opted to use
the term Generosity instead.
Under the voluntary wealth redistribution paradigm, Gatherers possess a “generosity” attribute. “Generosity” is a value
between 0 and 1, which represents the percentage of gathered sugar the Gatherer gives away to the poorest agent
within his vision range. The “generosity” values will be randomly selected at birth from a uniform distribution between
the pre-set minimum and maximum possible Generosity values established for a given simulation.
Warrior agents are neither taxed nor do they donate sugar.
This is because only income-sugar can be taxed or donated,
and Warriors do not themselves gather sugar (i.e. they have
no explicit income). As a reminder, since Enemies are not
considered agents in our environment, they do not gather,
consume, donate, or pay sugar taxes. As is the case with
Gatherers, when a Warrior dies, a new Warrior is spawned
at a random location in the world; this dynamic ensures
that the ratio of Gatherers to Warriors remains constant
throughout the simulation.
Each tick, the Gatherer will set aside a sugar amount equivalent to his Generosity multiplied by the amount of sugar
he gathered on that tick. This set aside amount will grow
each tick until the Gatherer is within range of a suitable recipient. Gatherers will not give food away to an agent who
is richer than themselves (this is to prevent generous agents
from ”giving themselves to death” and to prevent a generous
agent working alone for several time ticks from unloading his
accumulated stash on the first agent who comes into view,
who may indeed be very rich). Additionally, when donating
sugar to another Gatherer or to a Warrior, a given Gatherer
will at most give away enough sugar to even out his own and
the recipient’s wealth (sugar holdings).
4.
EXPERIMENTS AND RESULTS
In order to gather a compelling amount of experimental
data, each simulation was run 50 times, for 500 time ticks
each. Therefore, and unless explicitly stated otherwise, from
figure 4 onward, all of the presented results and graphs display values obtained from and averaged over all 50 of the
conducted runs.
4.1
Replicating Basic Sugarscape
In order to ensure that our simulations were reliable and
directly comparable with Epstein’s Sugarscape model, we
start our tests by replicating basic Sugarscape according to
the specifications outlined briefly in section 2 and described
in detail in [5].
It should be noted that for experiments with both forced
(Taxation-based) and voluntary (Generosity-based) wealth
redistributions, taxes are always to be extracted from the full
amount of sugar obtained during a given tick by a Gatherer,
while the portion of sugar to be donated is extracted as
a percentage of the sugar-income AFTER taxes have been
collected.
3.3
Neither agent type (Gatherers or Warriors) can perform the
duties of the other. Enemies will periodically enter the environment at random locations and attack nearby agents.
Gatherers will depend on Warriors to maintain the safety
of their environment in order to continue gathering sugar,
while Warriors will depend on Gatherers to gather and share
the sugar. Thus the survival of the society is dependent on
the cooperation among its members. Specifically, the wealth
created by the gathering of sugar must be redistributed or
the Warriors will die, and Enemies will destroy the Gatherers, thus wiping out the simulated society. Focusing on
wealth redistribution as the guiding force behind the emergence of collaboration in this decentralized model, we will
test and compare two different methods of such redistribution: voluntary (i.e. donations) vs mandatory (i.e. taxes).
To validate our model we compare it to that of Epstein and
Axtell [5] by calculating the Gini Coefficient, “a summary
statistic relating to inequality of income or wealth... It has
the desirable property that it does not depend on an underlying distribution ” [5]. The Gini Coefficient (or Gini index)
can be intuitively understood as it relates to the Lorenz
curve: “a plot of the fraction of total social wealth (or income) owned by a given poorest fraction of the population.
Any unequal distribution of wealth produces a Lorenz curve
Enemies & Warriors
We are extending the basic Sugarscape model [5] to include
three types of agents: Gatherers, which gather food from
the environment (these correspond to the turtles in Epstein’s original model), Warriors, who attack Enemies in the
60
Agent Vision Radius
Agent Metabolism
Agent Fortitude
Agent Lifespan
Population Size
Sugar Regrowth Rate
90
# Agents
75
60
45
Table 1: Parameters used for the Baseline Sugarscape experiment. (Population value has been
changed from 250 to 200 agents. The fortitude attribute was not part of Epstein and Axtell’s original
implementation [5])
30
15
0
0
10 20 30 40 50 60 70 80 90 100
Wealth Percentile
4.2
100
80
Additionally, we introduced fortitude to replace initial sugar
holdings provided at birth. Fortitude produces identical behavior to the latter approach, however, it leaves statistics
such as the Average Sugar Over Time and the Gini Coefficient unaffected, i.e. wealth generated over the agents’ life
time is not skewed by any initially “gifted” sugar amount.
Wealth statistics are therefore purely representative of agent
income. From this point onward, this slightly modified Sugarscape will be referred to as Baseline Sugarscape, and will
serve as the point of comparison for our models with wealth
redistribution.
60
40
20
0
0
20
40
60
80
Adjusting Sugarscape:
A Baseline for Comparison
Before testing our extensions to the Sugarscape domain (i.e.
Taxation and altruism), we first made a few small changes.
We lowered population size to 200 (from the original value of
250, which was shown to be close to the environment’s carrying capacity [5]) so as to simplify initial survival, since we
plan to make life on the Sugarscape more difficult through
the inclusion of non-gathering Warriors (who will need to be
fed by the Gatherers) and the increased metabolic rates in
the wounded Gatherers.
Figure 2: Wealth Distribution obtained by replicating Epstein and Axtell’s Sugarscape [5] (a typical
run)
% Wealth
1-6 spaces
1-4 sugar
5-25 sugar equivalent
60-100 ticks
200 agents
1 sugar per tick
100
% Population
The parameters presented in table 1 were held constant for
all of the experiments described in this paper. The chosen parameter values are identical to those used in Epstein
and Axtell’s Sugarscape, with the exception of population
size. Fortitude values were chosen to be identical to Epstein
and Axtell’s initial sugar holdings parameter, i.e. the sugar
provided to agents at birth.[5]
Figure 3: Lorenz Curve (corresponding to the
wealth distribution obtained by replicating Epstein
and Axtell’s Sugarscape [5] and depicted in figure 2)
that lies below the 45◦ line... The Gini ratio is a measure of
how much the Lorenz curve departs from the 45◦ line.”[5]
We present results averaged over 50 runs, which describe
in detail the behavior of Sugarscape without any form of
wealth redistribution. Figure 4 depicts the average Gini Coefficient obtained at each tick of simulation. The first 250
ticks of simulation display a rugged curve which corresponds
to fluctuations in wealth disparity. These fluctuations can
be explained by the fact that at tick 0, a batch of 200 agents
is born at the same time, and thus their birth times are
synced. This leads to a population-level behavior where
large groups of agents die around the same time and are
thus reborn around the same time (figure 5). Since newborn
agents begin life with 0 initial sugar, it appears as though
there is a large wealth disparity between newborns and the
older agents. As the simulation progresses, birth times become less synced and the Gini Coefficient reaches an equilibrium value of 0.61 (table 2). This is around 0.1 higher
The sugar wealth distribution for a typical run of the replicated Sugarscape is displayed in figure 2. The bar heights
correspond to the number of agents whose cumulative wealth
represents the corresponding wealth percentile. The graph is
heavily skewed toward the right, indicating that most agents
in the population have relatively low sugar reserves. By
looking at the right-most bar we can see that about 10 (out
of 200) agents hold 10% of the overall wealth, while the leftmost bar indicates that another 80 agents altogether also
hold 10%. The Lorenz Curve obtained from this wealth distribution is depicted in figure 3. The calculated Gini Coefficient corresponding to this curve is 0.4978 (Epstein’s value
fluctuated close to 0.50). Overall, we observed identical behaviors to those reported by Epstein and Axtell [5], thus
verifying our Sugarscape replica.
61
than the corresponding value in [5]. However, the higher
value does not imply a different behavior. This difference is
be explained by the fact that initial sugar holdings are absorbed into the fortitude attribute and thus do not influence
the Gini Coefficient.
1.0
Gini Index
0.8
Figure 5 depicts the average death rates across the population, calculated as a moving average with a window size
of 20 ticks. Death statistics are divided by cause of death.
Deaths by starvation tend to peak following a peak in deaths
by old age. This correlation implies that there is a period
of “pruning” following a wave of births during which inadequate agents (those with high metabolic rates and those
with a small vision radius born into a low-sugar area) die of
starvation. These peaks become less pronounced as births
de-synchronize over time. Eventually, both death rates reach
the equilibrium values reported in table 2.
0.4
0.2
0.0
0
100
200
300
400
500
Tick
Figure 6 depicts the average individual sugar holdings in the
population at each tick of simulation. This value peaks at
tick 60, at which point the average age in the population
is the highest it will ever be. This is caused by the synced
birth times and the predetermined minimum lifespan of 60
ticks. Older agents tend to have a larger sugar holding because they have had more time to collect wealth. At tick 60,
agents begin to die of old age and are replaced by newborns
with 0 sugar, thus lowering the average across the population. As was the case with the Gini coefficient and with the
average death rates, average sugar holdings eventually reach
an equilibrium value (reported in table 2).
Figure 4: Gini Coefficient over time, simulated on
the Baseline Sugarscape model.
# Deaths per Tick
10
Figure 7 depicts the average productivity of individual agents
at each tick of simulation, while figure 8 depicts the total
sugar produced and consumed by the population at each
tick of simulation. Productivity is calculated on each tick
according to equation 1 and is measured in units of sugar.
Productivity serves as a measure of the degree to which the
population has optimized by eliminating inefficient individuals (allowing them to starve). Figure 8 provides a more
detailed view of the same concept and describes whether a
drop in productivity is caused by a drop in total production or a rise in total consumption. All tracked statistics in
these figures reach equilibrium values, which are reported in
table 2.
totalproduction − totalconsumption
(1)
numberof agents
Starvation
Old Age
8
6
4
2
0
0
100
200
300
400
500
Tick
Figure 5: Average deaths over time, simulated on
the Baseline Sugarscape model. Average deaths per
tick are calculated as a moving average with a window size of 20 ticks.
4.3
P roductivity =
0.6
Extending Sugarscape:
Wealth Redistribution on the Sugarscape
without Warriors or Enemies
This section describes a set of experiments that serve to compare two different methods of wealth redistribution: Generosity and Taxation. Both methods were run 50 times with
each of 10 different values for average Generosity and tax
rate, respectively. The average equilibrium values1 of the
statistics introduced in section 4.2 for each set of runs are
compared. Please note for ease of comparison with our established Baseline Sugarscape model (section 4.2), that the
results of table 2 are also included in the graphs of section 4.3.1 (figures 9, 10, 11, 12, and 13) as 0% Average
Generosity (left-most point on the curves) and the graphs
of section 4.3.2 (figures 14, 15, 16, 17, and 18) as 0% Tax
All of the simulations presented in section 4.3 reached equilibrium values for all of the measured statistics during the
last few hundred ticks of simulation, following an initial period of roughness. As such, the behavior of each set of parameters with respect to a given statistic can be summarized
by a single numerical value: the value of the equilibrium position obtained at the end of the simulation for that statistic.
Equilibrium values for the “baseline” parameter settings in
this section are reported in table 2 and serve as a point of
comparison for the experiments in section 4.3.
1
Equilibrium values are the stable values reached and maintained for the last few hundred ticks of a simulation.
62
700
50
600
500
40
Sugar
Average Sugar
60
30
20
300
Total Production
Total Consumption
200
10
100
0
0
0
100
200
300
400
500
0
Tick
100
200
300
400
500
Tick
Figure 6: Average sugar-holdings over time, simulated on the Baseline Sugarscape model.
Figure 8: Total Sugar Produced vs. Consumed over
time, simulated on the Baseline Sugarscape model.
Average Productivity
Total Production
Total Consumption
Deaths from Starvation
Deaths from Old Age
Deaths from Violence
Gini Coefficient
2
Average Productivity
400
1
0
0.8768
584.54
409.18
1.461
2.236
0.0
0.6110
Table 2: Final values for experiment conducted on
the Baseline Sugarscape model. (Results were obtained by averaging 50 runs of 500 ticks each).
-1
-2
0
100
200
300
400
500
100%-100%, thus obtaining the missing average Generosities
of 60%, 70%, 80%, 90%, and 100%. The reasoning for choosing these ranges instead of other options that would result
in equivalent average values (e.g. for an average Generosity
of 80%, the range of 60%-100% was tested instead of 70%90%) was the strive to maximize the variance of the Generosity values for each simulation. We felt the experimental
results would be less synthetic, and thus more representative of the real world, if the maximum possible amount of
natural stochasticity was preserved during the tests.
Tick
Figure 7: Average Productivity over time. (Baseline
Test)
Rate (once again, corresponding to the left-most point).
4.3.1
Generosity-Based Wealth Redistribution
(Sugarscape without Warriors or Enemies)
Results. As we mentioned in the Setup section, the average
Setup. For this experiment we incorporated the Generositybased wealth redistribution method (defined in section 3.2)
into our Baseline Sugarscape model (described in section 4.2).
Initially 50 simulation runs (of 500 ticks each) were performed for each of the following Generosity percentage ranges
(the format being minimum possible value - maximum possible value): 0%-20%, 0%-40%, 0%-60%, 0%-80%, 0%-100%.
For every tested range, the observed average Generosity was
fluctuating slightly (+1%) center of the range (i.e. 10%,
20%, 30%, 40%, and 50%, respectively). However, this
left untested some of the other potentially interesting average Generosity values. Consequently, additional tests with
higher minimum values were also performed, namely those
for ranges 20%-100%, 40%-100%, 60%-100%, 80%-100%, and
63
Generosity values across all agents fall right in the middle of
the ranges of allowed Generosity values. This result showcases that on average agents are not dying from being overly
generous (i.e. giving away all of their sugar). Instead, agents
who give away their sugar are saved by donations from other
generous agents. Had this not been the case, the observed
average Generosity values would fall below the middle of the
ranges, as the most generous individuals (those with top-ofthe-range Generosity values) would be less likely to survive.
Figure 9 depicts the Gini Coefficient for each rate of average Generosity between 0% and 100%, in increments of
10%. Predictably, as Generosity increases (i.e. as agents
give away more of their sugar), the Gini Coefficient decreases, corresponding to a decrease in wealth inequality.
However, from 0% to 10% Generosity, there is a marked
increase in the Gini Coefficient. This phenomenon is explained by wealthy agents in high-sugar areas donating just
enough of their income to prevent agents with high sugar
metabolisms from starving to death. Without these donations, such high-metabolism agents would have died, getting
an opportunity to be reborn as agents with a stronger ability to accumulate wealth (i.e. with a lower metabolic rate or
with a higher vision radius). Figure 13 corroborates this explanation: from 0% to 10% Generosity, the total consumption of the population increases significantly, which corresponds to an increase in the survival rate of high-metabolism
individuals. Figure 10 further supports our reasoning: from
0% to 10% Generosity, the number of deaths via starvation
decreases significantly (while the number of deaths via old
age increases as a consequence).
1.0
Gini Index
0.8
0.6
0.4
0.2
0.0
0
10 20 30 40 50 60 70 80 90 100
Average Generosity (%)
The Generosity model of wealth redistribution demonstrates
an ability to decrease wealth inequality while simultaneously
maintaining a productive (figure 12) and wealthy (figure 11)
society. However, at all levels of Generosity, a significant
number of agents die of starvation (figure 10). These deaths
serve to prune the unproductive members from the population; namely, only those agents who reside within a reasonable range from the high-sugar areas of the landscape actually receive significant assistance. The Generosity model
thus distils the population down to only those agents who
are most productive. As such, the total production curve
remains at a maximum constant level regardless of the average Generosity of the population (figure 13). While the
Generosity model has its advantages, a significant number
of deaths due to starvation is generally unacceptable in a
modern society.
Figure 9: Gini Coefficient vs. Generosity Percentage for the Generosity-Based Wealth Redistribution
experiment.
# Deaths per Tick
3
2
Starvation
Old Age
1
0
A curious phenomenon is observed in figure 11: as Generosity increases past 10%, the agents’ average sugar holdings
continually increase, even reaching levels beyond the baseline value (at 0% Generosity). The curiosity lies in the fact
that such a high level of average sugar holding is achieved at
the same time that average productivity reaches its lowest
point. This phenomenon is explained by a closer look at the
behavior of generous agents, who always donate to agents
less wealthy than themselves. Since older agents tend to
have the highest accumulated wealth (due to having more
time to accumulate sugar), donation recipients tend to be
the younger agents. In a society where a larger proportion of income is donated, more income is directed towards
younger agents. As a result, in a 100% generous society,
agents are brought up to the average sugar holding within
the first few ticks of their life. Since wealth is not inherited,
and thus disappears upon death, donating to the younger
members of the population serves to preserve the donated
wealth, protecting it from being destroyed. Therefore, a
greater proportion of society’s wealth is “indirectly inherited” by future generations at higher levels of Generosity.
This dynamic may change if the model is modified to explicitly include a mechanism for inheritance.
0
10 20 30 40 50 60 70 80 90 100
Average Generosity (%)
Figure 10: Average deaths vs. Generosity Percentage for the Generosity-Based Wealth Redistribution
experiment. Average deaths per tick are calculated
as a moving average with a window size of 20 ticks.
Setup. For this experiment we have incorporated the Taxationbased wealth redistribution method (defined in section ??)
into our Baseline Sugarscape model (described in section 4.2).
A total of 11 separate simulations were performed, one for
each of the following Taxation percentages: 0%, 10%, 20%,
30%, 40%, 50%, 60%, 70%, 80%, 90%, and 100%. While
these values do discretize the range of all possible Taxation
levels, the reader will notice (by observing the graphs in the
following Results section) that they nevertheless produce a
smooth gradient for all of the presented measurement metrics. Each simulation was once again performed 50 times,
and allowed to run for 500 ticks.
Results. Figure 14 depicts the Gini Coefficient for each Tax
4.3.2
rate between 0% and 100%, in increments of 10%. As the
Tax rate increases, the Gini Coefficient decreases because
progressively more wealth is being redistributed. However,
Taxation-Based Wealth Redistribution
(Sugarscape without Warriors or Enemies)
64
60
40
30
20
10
1.2
0
Average Productivity
0
10 20 30 40 50 60 70 80 90 100
Average Generosity (%)
Figure 11: Average sugar-holdings vs. Generosity
Percentage for the Generosity-Based Wealth Redistribution experiment.
there is an increase in the Gini Coefficient between 0% and
30% Tax rates. This occurs because Taxes serve to prevent the deaths of the least adequate individuals (who would
have died without the “welfare” provided by the Tax system).
The decrease in deaths due to starvation shown in figure 15
proves that starving agents are being saved. Consequently,
their low sugar holdings persist in the population, bringing
down the observed average sugar (figure 16), while simultaneously raising wealth inequality (figure 14). Logically,
average productivity also decreases as more of these inadequate agents are saved from starvation (figure 17). As the
Tax rate increases past 30%, the Gini Coefficient rapidly decreases to a value below 0.1, which corresponds to a society
where all agents have nearly identical levels of wealth.
1.0
0.8
0.6
0.4
0.2
0.0
0
10 20 30 40 50 60 70 80 90 100
Average Generosity (%)
Figure 12: Average Productivity vs. Generosity
Percentage for the Generosity-Based Wealth Redistribution experiment.
700
600
500
As was the case with Generosity, as Taxation increases, average sugar holdings decrease steadily, reach a minimum, and
then increase again (figure 16). Once again, the cause for
this phenomenon is the preservation of the wealth of older
individuals through its redistribution to the younger members of the population. In fact, the Tax-based system is even
more adept at this redistribution than the Generosity-based
system since welfare can always reach the least wealthy (thus
reaching every newborn), which is not true of the Generositybased system (since donations are restricted to visible neighbors). However, the effect is less pronounced because there
is less wealth to go around (as demonstrated by the low
average productivity at high tax rates in figure 17).
65
Sugar
Average Sugar
50
400
300
200
Total Production
Total Consumption
100
0
0
10 20 30 40 50 60 70 80 90 100
Average Generosity (%)
Figure 13: Total Sugar Produced and Consumed
vs. Generosity Percentage for the Generosity-Based
Wealth Redistribution experiment.
60
0.8
50
Average Sugar
Gini Index
1.0
0.6
0.4
0.2
0.0
40
30
20
10
0
0
10 20 30 40 50 60 70 80 90 100
0
Tax Rate (%)
10 20 30 40 50 60 70 80 90 100
Tax Rate (%)
Figure 14: Gini Coefficient vs. Tax Rate for the
Taxation-Based Wealth Redistribution experiment.
Figure 16: Average sugar-holdings vs. Tax Rate for
the Taxation-Based Wealth Redistribution experiment.
1.2
Average Productivity
# Deaths per Tick
3
2
Starvation
Old Age
1
0
0
10 20 30 40 50 60 70 80 90 100
1.0
0.8
0.6
0.4
0.2
0.0
Tax Rate (%)
0
10 20 30 40 50 60 70 80 90 100
Tax Rate (%)
Figure 15: Average deaths vs. Tax Rate for the
Taxation-Based Wealth Redistribution experiment.
Average deaths per tick are calculated as a moving
average with a window size of 20 ticks.
4.4
Figure 17: Average Productivity vs. Tax Rate for
the Taxation-Based Wealth Redistribution experiment.
Extending Sugarscape:
Enemies & Warriors
After both Taxation-based Sugarscape and Generosity-based
Sugarscape have been tested, these wealth redistribution
paradigms will now be tested on a more realistic model,
i.e. the Warrior-Enemy Sugarscape model detailed in section 3.3. These additional tests were conducted in order
to establish the dependency of the results obtained in section 4.3 on the specifics of the Baseline Sugarscape model.
We believe that incorporating hardship into the model (such
as violence through Enemy agents, and free-loaders or imposed public services through Warrior agents) represents a
society closer to the real world than Baseline Sugarscape.
Additionally, if agent behaviors were to be evolved through,
for example, an Evolutionary Algorithm, a society that has
no need to support free-loaders (Warriors do not gather
sugar, but they do consume it) or to contribute toward funding of public services (Warriors protect Gatherers from Enemies) would simply evolve to not be ”generous”, or to collect
66
lower taxes, allowing agents who are less able to collect sugar
to die out.
In the real world, however, we generally regard Life above
all else, and thus protecting individuals who are unable to
provide for themselves has often affected public policy (e.g.
welfare in the U.S.). Furthermore, following John Donne’s
famous line ”No man is an island...”, it is evident that as societies have become more complex, individuals have become
increasingly dependent on functions performed by others.
For these reasons, it is sensible to conduct wealth redistribution tests on a model that would more closely resemble
both the human concern for the well-being of the community, and the idea of an agent needing other agents (or, in
our case, other types of agents) to survive.
In all of the following experiments Enemy agents are spawned
at a constant rate of 0.5 Enemies per time tick (i.e. every
60
600
50
Average Sugar
700
Sugar
500
400
300
200
Total Production
Total Consumption
100
40
30
20
10
0
0
0
10 20 30 40 50 60 70 80 90 100
0
Tax Rate (%)
200
300
400
500
Tick
Figure 18: Total Sugar Produced and Consumed vs.
Tax Rate for the Taxation-Based Wealth Redistribution experiment.
Figure 19: Average sugar holdings for each time
step, averaged over 50 runs on the Warrior-Enemy
Sugarscape without Taxation and with an average
Generosity of 20%.
tick there is a 50% chance that an Enemy will spawn; therefore, on average, one Enemy is spawned every two ticks).
A constant 1 to 9 Warrior to Gatherer ratio is maintained
throughout each simulation (i.e. 10 % of our 200 agents are
Warriors). This value was chosen because preliminary tests
showed it to be near the maximum percentage of Warriors
that our Gatherer population could support. Preliminary
tests also revealed that this percentage of Warriors could
prevent the Enemy population from spiking (thus preventing spikes in the observed death rates) at a maximum rate
of 0.5 Enemies/tick. These parameter values impose a constant yet manageable level of hardship on the population,
without causing additional complicated dynamics (such as
cyclic increases and decreases in population death rates due
to violence or starvation).
4.4.2
Generosity-Based Wealth Redistribution
in the Warrior-Enemy Sugarscape
Setup. For this experiment we have added the Generositybased wealth redistribution method (defined in section 3.2)
to our Warrior-Enemy Sugarscape model (described in section 3.3). Just as in before (section 4.3.1), we systematically
tested the following Generosity percentage ranges: 0%-20%,
0%-40%, 0%-60%, 0%-80%, 0%-100%, 20%-100%, 40%-100%,
60%-100%, 80%-100%, and 100%-100%.
Results. The simulations conducted on the Warrior-Enemy
Sugarscape display a Gini Coefficient that steadily decreases
as average Generosity increases (depicted in figure 20), which
tells us that within this model, just like in its violence-free
counterpart, the sugar holdings are becoming less varied
throughout the population as agents donate more and more
of their income.
Unlike the Sugarscape variations without Warriors and Enemies, the Warrior-Enemy Sugarscape never reached the
near-perfect equilibrium values. Figure 19 depicts the average sugar holdings each tick, averaged over 50 runs of the
Warrior-Enemy Sugarscape with an average Generosity of
20%. The system did not converge to a single equilibrium
value (or near one) by generation 500, oscillating indefinitely
with a small amplitude. Consequently, in order to perform
the same tests as before, the last 200 ticks of all 50 runs
were averaged to obtain a single value for each of the Tax
and Generosity rates described in sections 4.3.1 and 4.3.2.
4.4.1
100
Yet again we see a different behavior for Generosity under 10% (the Gini Coefficient actually increases for this
range). This can be explained by looking at the corresponding deaths graph (figure 21): deaths by starvation decrease, while deaths from old age slowly increase. Since
some sugar is being donated at 10% Generosity, some of
the least wealthy agents are being saved from starving to
death. The survival of the poorest individuals through common wealth decreases the overall average sugar (figure 22).
It also increases consumption (figure 24), which, since production is unaffected by the decrease in deaths of low-sugar
producing agents, causes a decrease in the overall productivity (figure 23). Put simply, under-producers are protected
through the Generosity-based wealth redistribution, while
over-consumers are not, just as was the case in the Warriorfree simulations displayed in figure 13).
0% Generosity and 0% Taxation
in the Warrior-Enemy Sugarscape
The experiment on the Baseline Sugarscape model with a
Generosity level of 0% and a Taxation level of 0% is implicitly included in the results of the following two sections. A
Warrior-Enemy Sugarscape without Generosity is plotted on
the curves of section 4.4.2 (figures 20, 21, 22, 23, and 24)
as 0% Average Generosity (left-most point on the curves).
Similarly, a Warrior-Enemy Sugarscape without Taxation is
represented on the graphs of section 4.4.3 (figures 25, 26,
27, 28, and 29) as 0% Tax Rate (once again, corresponding
to the left-most point).
Noticeably different values can, however, be observed when
67
comparing the starvation death rates of the Warrior-Enemy
Sugarscape vs those of its Warrior-less counterpart (figure 21
vs figure 10). The much higher initial rate of deaths due to
starvation is caused by the inclusion of free-loading Warriors,
who depend on stumbling around the map, getting fortuitous donations in order to survive. Warriors’ life prospects
are especially grim at 0% Generosity: with no donations
from altruistic Gatherers, Warriors can only survive for a
few ticks (depending on their individual fortitude). At a
Generosity levels of 10% and 20% it is still difficult for Warriors to survive. Yet another new feature is the existence
of a small but constant rate of deaths due to violence, as
Enemies now roam throughout the simulated world (notice
the flat dashed line in figure 21).
# Deaths per Tick
4
Starvation
Old Age
Violence
3
2
1
0
0
10 20 30 40 50 60 70 80 90 100
Average Generosity (%)
Once again we see a small rise in average sugar (figure 22)
through the previously described communal inheritance-like
behavior, where a higher average Generosity corresponds to
more sugar being passed on to the least wealthy (including
newbors) , and thus less sugar disappearing upon an agents’
death from old age (section 4.3.1).
Figure 21: Average deaths vs. Generosity Rate
for a Generosity-Based Wealth Redistribution in the
Warrior-Enemy Sugarscape model. Average deaths
per tick are calculated as a moving average with a
window size of 20 ticks.
1.0
Gini Index
0.8
Warrior agents (figure 14), but instead bottoms out at a
much higher value of 0.25 for the Taxation rates above 70%
(please view figure 25). The cause for this higher observed
wealth disparity is as follows: when taxes above 70% are
being collected, most of the sugar is spread among the least
wealthy individuals. However, since the collected amount is
comparatively high, the population becomes highly equalized in terms of agent’ individual sugar-wealth.
0.6
0.4
0.2
0.0
0
Once taxes are distributed, agents consume the amount corresponding to their metabolic rates, consequently obtaining
different left-over sugar amounts, which now constitute their
wealth. At such high Taxation rates, however, average sugar
levels become extremely low (3-4 units of sugar in figure 27
for top 4 Taxation rates), which leaves the average agent
near starvation. The corresponding death rate graph (figure 26) shows that deaths from starvation at these high Tax
levels are quite low (about 0.2 per tick), but can never reach
0.0 as there simply isn’t enough sugar to go around when
no agent is pruned from the population for it’s individual
shortcomings.
10 20 30 40 50 60 70 80 90 100
Average Generosity (%)
Figure 20: Gini Coefficient vs. Generosity Rate
for a Generosity-Based Wealth Redistribution in the
Warrior-Enemy Sugarscape model.
4.4.3
Taxation-Based Wealth Redistribution
in the Warrior-Enemy Sugarscape
Setup. For this experiment we have added the Taxationbased wealth redistribution method (defined in section ??)
to our Warrior-Enemy Sugarscape model (described in section 3.3). As with previous Taxation-Based tests (section 4.3.2),
we once again simulated the same 11 Taxation levels: 0%,
10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 100%.
Results. The following results were obtained from conducting 5 simulations (50 runs of 500 ticks each) on with the
Warrior-Enemy Sugarscape extended by a Taxation-Based
Wealth Redistribution.
The Gini Coefficient does not converge to a value near 0.1,
as it did during our simulations on the Sugarscape without
68
The highest Taxation levels for this experiment quite elegantly simulate a Communist-like society, where everyone
is equally poor and just barely manages to get by on the
small equal amounts of goods doled out by the government,
which is in charge of collecting and managing all individual
incomes. As depicted in figure 29, production lowers and
consumption rises until the two become equalized, which,
in combination with a near 0.0 productivity (shown in figure 28) is indicative of an impoverished society, in which
agents’ lives are more perilous, and shorter, as showcased
by lower reachable deaths from old age, as compared to
those observed in the corresponding Warrior-less experiment
(compare figure 26, for the former, vs figure 15, for the latter). without our instant rebirth dynamic and the fortitude
amounts provided at birth, his society would not survive.
700
50
600
500
40
Sugar
Average Sugar
60
30
20
400
300
200
10
Total Production
Total Consumption
100
0
0
0
10 20 30 40 50 60 70 80 90 100
0
Average Generosity (%)
10 20 30 40 50 60 70 80 90 100
Average Generosity (%)
Figure 22: Average sugar-holdings vs. Generosity
Rate for a Generosity-Based Wealth Redistribution
in the Warrior-Enemy Sugarscape model.
Figure 24: Total Sugar Produced and Consumed
vs. Generosity Rate for a Generosity-Based Wealth
Redistribution in the Warrior-Enemy Sugarscape
model.
Average Productivity
1.2
in figure 13, total sugar consumption increases while total
production remains constant.
1.0
0.8
As to the Warrior-Enemy Sugarscape model, some pronounced
differences emerged during experimental analysis. At highest taxation rates, an artificially inflated Gini Coefficient
implies high disparity in wealth among the agents, while in
reality the entire population is quite poor, and remains at a
constant near-starvation point. Consequently some agents
are consistently lost to death by starvation. This is in constant to the Warrior-free model, which at Tax rates about
40% avoids all starvation deaths. This may indicate that
the Warrior-Enemy model is in fact more realistic, by constantly imposing some level of hardship on the population.
Additionally, a steadily decreasing average sugar value was
observed in a the simulation with Warrior agents, all the
way down to a population-wide starvation (figure 27), while
in the Warrior-free experiment, the value for 100% Tax rate
was nearly 20 units of sugar per agent. These results can
be verified intuitively since a population with explicitly freeloading Warriors who need to be fed is much harder to maintain at a higher level of wellbeing. (For a visual comparison,
please refer to figures 15 and 26).
0.6
0.4
0.2
0.0
0
10 20 30 40 50 60 70 80 90 100
Average Generosity (%)
Figure 23: Average Productivity vs. Generosity
Rate for a Generosity-Based Wealth Redistribution
in the Warrior-Enemy Sugarscape model.
5.
DISCUSSION
According to the results obtained in sections 4.3.2 and 4.3.1
from experiments conducted on the Baseline Sugarscape, the
Taxation-based wealth redistribution achieves a much lower
Gini Coefficient than a Generosity-based system. Taxation
also completely eliminates death by starvation around the
50% Tax rate, while Generosity stagnates at an average of
0.5 deaths per tick. However, the Taxation system produces
a society with significantly lower productivity: 0.2 sugar per
tick vs a productivity of 0.5 for its Generosity counterpart).
When comparing the Generosity-based wealth redistribution
on Warrior-Enenemy Sugarscape vs the Sugarscape without
Warriors or Enemies, the expected higher levels of starvation
deaths were observed at low Tax rates in the Warrior-Enemy
Sugarscape. Equally anticipated lower productivity values
and lower average sugar values were reported for this model
(as Warriors cannot gather sugar).
Yet another difference between the two wealth redistribution methods is the fact that Taxation protects both overconsumers and under-producers from starvation , while a
Generosity-based wealth redistribution saves over-consumers
only. This is evidenced in figure 18 by an increase in total consumption and a decrease in total production, as Tax
rate increases. On the other hand, as Generosity increases
69
Results obtained in [2] suggest that redistributing wealth
in an ”equal shares” way (everybody has equal access to a
portion of the total reward) as opposed to a ”proportional
to input” way (everybody receives reward proportional to
their input towards producing that reward) causes the emergence of freeloaders. We corroborate this result in our model
in which the Tax-based approach corresponds to an ”equal
4
# Deaths per Tick
1.0
Gini Index
0.8
0.6
0.4
0.2
0.0
2
Starvation
Old Age
Violence
1
0
0
10 20 30 40 50 60 70 80 90 100
0
Tax Rate (%)
10 20 30 40 50 60 70 80 90 100
Tax Rate (%)
Figure 25: Gini Coefficient vs.
Tax Rate for
a Taxation-Based Wealth Redistribution in the
Warrior-Enemy Sugarscape model.
Figure 26: Average deaths vs.
Tax Rate for
a Taxation-Based Wealth Redistribution in the
Warrior-Enemy Sugarscape model. Average deaths
per tick are calculated as a moving average with a
window size of 20 ticks.
shares” wealth redistribution that is plagued by freeloaders
and the Generosity-based approach corresponds to a ”proportional to input” wealth redistribution. Generosity corresponds to ”proportional to input” because in order to receive
a donation, an agent must be within a short distance from
a rich agent, which likely means that the recipient agent is
himself producing a relatively high amount of sugar (due
to the way that the landscape is laid out: high-sugar areas
exist in large clusters).
6.
3
This success is achieved by removing those members of society who do not contribute. When financial and physical
strain is instead added to a society with a Tax-based method
of wealth redistribution, the society may suffer greatly. The
Tax-based method attempts to feed every agent that is born
without regard to whether or not it is possible to do so. In
the event that it is not possible to feed everyone, the entire society crumbles (as demonstrated in section 4.4.3). At
high tax rates, a strained society ceases to be productive and
loses all of its wealth, suffering a constant trickle of deaths
by starvation. Such characteristics are indicative of poverty.
CONCLUSIONS
Based on our experiments, it is clear that both taxation and
altruism are powerful tools with which a society may redistribute wealth. As we have demonstrated, both methods
significantly impact the Gini index, death rates, productivity, and average wealth of a society. However, each method
acts on these factors in a fundamentally different way.
While it would certainly be unethical to encourage a purely
Generosity-based approach to wealth redistribution in the
real world (in the hopes that the least productive members
of society die of starvation), Generosity should not be dismissed entirely. As demonstrated in this paper, Generosity
has the ability to redistribute wealth in a powerful way that
is on par with Taxation. On the other hand, while many human societies value Life about all else, employing a purely
Tax-based approach would be detrimental to our productivity, thus lowering the quality of said valuable Life.
Our results indicate that a Tax-based approach to wealth
redistribution produces a sharper decrease in the Gini index than a Generosity-based approach at very high levels
of wealth redistribution (above 70%). However, at low to
moderate levels of wealth redistribution (e.g. 30%), Generosity actually achieves a lower Gini index than Taxation.
At all levels of wealth redistribution, Generosity is able to
maintain a significantly higher productivity and standard of
living within the society than Taxation. These advantages
come at the expense of agents’ lives. The Tax-based approach to wealth redistribution achieves a starvation death
rate of nearly 0 with only a 40% tax rate. On the other hand,
the Generosity-based approach never removes starvation entirely. Rather, Generosity-based wealth redistribution uses
starvation as a tool to achieve higher productivity by removing inefficient members from the population.
The results observed during our experiments cannot be assumed reliable when regarded as strictly numerical data, due
to the sheer simplicity of the underlying model. The observed phenomena can however be intuitively verified through
reasoning and through connections drawn between each of
the five data curves obtained for each of our experiments.
For example, and as previously mentioned, it is self-evident
that a model under which a population experiences hardships in the form of free-loaders and outside-attacks, while
also paying Taxes at a rate of 100% clearly corresponds (albeit in a somewhat naive way) to a Communist-like society. From this perspective, all of the accompanying socioeconomic behaviors observed during the corresponding experiment make intuitive sense, if one considers, for instance,
the hardships endured by the commoners in the former USSR.
When additional financial and physical strain is added to
a society with a Generosity-based method of wealth redistribution, the society thrives. The wealth redistribution in
such a society is able to lower the death rates, lower the
Gini index, and maintain productivity and average wealth.
70
700
50
600
500
40
Sugar
Average Sugar
60
30
20
300
200
10
Total Production
Total Consumption
100
0
0
0
10 20 30 40 50 60 70 80 90 100
0
Tax Rate (%)
Figure 29: Total Sugar Produced and Consumed vs.
Tax Rate for a Taxation-Based Wealth Redistribution in the Warrior-Enemy Sugarscape model.
Taxation or Generosity rates we can obtain insights into the
benefits and side-effects of the different possible wealth redistribution paradigms that a society could employ to better
the quality of life, increase productivity, or to lower death
rates. These results are especially promising due to the way
our minimal extensions to the Sugarscape model ([5]) are
able to provide such comparatively large insights into the
dynamics of human economic interaction. Nevertheless, all
models have their limitations, and the extended Sugarscape
presented here is no exception. For example, our model is
simulated as a closed system, while that hardly ever the case
with real world societies (especially those we would consider
interesting to model in the first place). We do however hope
that our significant returns on the comparatively small investment (of incorporating two distinct wealth redistribution
mechanisms into the very simplistic original Sugarscape) will
inspire others to extend simple economic models (including
the Warrior-Enemy Sugarscape presented here), try to make
sense of the observed phenomena, and share their insights
with the community.
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
10 20 30 40 50 60 70 80 90 100
Tax Rate (%)
Figure 27: Average sugar-holdings vs. Tax Rate
for a Taxation-Based Wealth Redistribution in the
Warrior-Enemy Sugarscape model.
Average Productivity
400
10 20 30 40 50 60 70 80 90 100
Tax Rate (%)
Figure 28: Average Productivity vs. Tax Rate
for a Taxation-Based Wealth Redistribution in the
Warrior-Enemy Sugarscape model.
7.
Alternatively, a society with relatively low taxation of 30%
which produces a very high Gini Coefficient of 0.7 (figure 25),
more closely resembles a Capitalist society, such as, for example, that of the current-day United States. However, U.S.
also possess some unknown to us level of average Generosity,
and thus its socio-economic interactions would be better approximated by a wealth redistribution model that combines
the mechanisms of Taxation and Generosity.
FUTURE WORK
In the future, we would like to conduct a more systematic
comparison of different Taxation and Generosity levels on a
more complex and thus hopefully a more realistic version of
our extended Sugarscape. The Wealth-Redistributing Sugarscape model can be augmented with countless extensions
in order to mold this simulation tool and adapt its applicability to the interests and needs of a motivated researcher.
There are many interesting questions that can be asked
about and investigated through simulations conducted on
the Wealth-Redistributed Sugarscape domain. For example, what happens when the Warrior-Enemy Sugarscape is
subjected to a “natural disaster” through a sudden (but not
too prolonged) increase in Enemy spawning rate? Another
option would be to test the Warrior-Enemy model through a
simulated “recession”, which would consist of lowered sugar
regeneration rates, a decrease in the maximum amount of
sugar available on any given patch, or both.
The main contribution of the work presented here is an extremely simple to both understand and implement model,
that in all of its bare-boned simplicity still manages to capture the overarching nature of a society of individuals interacting within an economy. We show that by incorporating
a very basic Taxation or Generosity mechanic, Epstein and
Axtell’s Sugarscape model achieves the ability to model a
trade of currency and services between the government and
its people; simultaneously, by testing some of the potential
71
One of the most interesting extensions would be to explore
different combinations of Taxation-based and Generositybased models, in order to discover whether the two wealth
redistributions can be combined in such a way so as to minimize their respective negative effects (such as deaths by
starvation or a high Gini Coefficient), while increasing positive phenomena (such as high average sugar holdings or
increased productivity).
8.
REFERENCES
[1] R. Axelrod. The evolution of cooperation: revised
edition. Basic books, 2006.
[2] R. Axtell. Non-cooperative dynamics of multi-agent
teams. In Proceedings of the first international joint
conference on Autonomous agents and multiagent
systems: part 3, pages 1082–1089. ACM, 2002.
[3] A. Bell, P. Richerson, and R. McElreath. Culture
rather than genes provides greater scope for the
evolution of large-scale human prosociality. Proceedings
of the National Academy of Sciences,
106(42):17671–17674, 2009.
[4] A. Delton, M. Krasnow, L. Cosmides, and J. Tooby.
Evolution of direct reciprocity under uncertainty can
explain human generosity in one-shot encounters.
Proceedings of the National Academy of Sciences,
108(32):13335–13340, 2011.
[5] J. M. Epstein and R. L. Axtell. Growing Artificial
Societies: Social Science from the Bottom Up. Complex
adaptive systems. The MIT Press, 1996.
[6] R. Trivers. The evolution of reciprocal altruism.
Quarterly review of biology, pages 35–57, 1971.
72
Cooperative Coevolution of a Heterogeneous Population of
Redditors
Lisa Soros
University of Central Florida
Orlando, FL, USA
lisa.soros@isl.ucf.edu
ABSTRACT
populations. Durkheim describes this cohesive persona as
the collective consciousness of a group [2]. Collective consciousness consists of the beliefs and normative structures
which are generally shared by members of a group. Though
some individuals may hold unique beliefs, there tend to be
at least some mores which characterize the group as a whole
(e.g., the Christian collective consciousness might be said to
espouse the Ten Commandments).
Online communities offer a unique venue for studying cultural phenomena. One such phenomenon is collective consciousness, in which a distinct persona emerges from a heterogeneous population. The collective consciousness of the
Reddit online community is modeled using a cooperative coevolutionary algorithm. The coevolutionary algorithm is applied to connection weights on fixed-topology artificial neural networks. Each neural network decides to upvote or
downvote actual Reddit content based on descriptive tags
and the elapsed time since submission. The cooperative
coevolutionary approach proves to be unsuccessful for the
target domain. Analysis shows that this outcome is largely
due to the high dimensionality of the search space. This
outcome also motivates further investigation into methods
for large-scale content categorization.
To understand the mechanics of collective consciousness is
to understand social solidarity. Why do members of online
communities identify so strongly with each other when they
don’t interact with each other in the physical world? As it
turns out, the anonymity afforded by online communication
increases identification with communities-at-large, though it
devalues connections between any given individuals [1].
Categories and Subject Descriptors
I.2.8 [Artificial Intelligence]: Problem Solving, Control
Methods, and Search—heuristic methods; I.2.11 [Artificial
Intelligence]: Distributed Artificial Intelligence—coherence
and coordination, multiagent systems; I.6.0 [Simulation and
Modeling]: General
General Terms
Experimentation
Keywords
Cooperative coevolution, neuroevolution, evolutionary algorithms, collective consciousness
1.
INTRODUCTION
Internet communities, unlike their offline counterparts, aren’t
defined by geographic constraints. As a result, they tend to
have more diverse populations than communities based on
face-to-face interactions [9]. Yet, such diversity does not
lead to disorder; in fact, a cohesive persona often emerges
from the interactions of individuals in these heterogeneous
This paper studies Reddit, a social news aggregator website whose members display phenomena such as collective
consciousness. Reddit users, called Redditors, submit links
to external websites that they find interesting. Other Redditors then review these links and then choose to upvote
(approve), downvote (disapprove), or abstain from voting
on the submissions. Each user is limited to one vote per
submitted link. The cumulative votes of the Reddit community determine if and where the link will be displayed on
the main Reddit page, with the most visible spots at the top
of the page displaying the links that collect the most votes.
From this mechanism, it becomes possible to discern a sense
of ”what Reddit likes” as a whole.
In 2011, Van Miegham analyzed the behaviors of Reddit
users and their voting patterns for submitted content [4].
This resulted in the Reddit Score, an analytical model which
predicts the number of upvotes and downvotes for an arbitrary piece of submitted content . Van Mieghem found that
the number of downvotes for a piece of content had a power
law -like relation to the number of upvotes. In fact, the
number of downvotes increases faster than the number of upvotes, which surprised Van Miegham and caused him to call
for a socio-psychological explanation of this phenomenon.
The goal of this research is to model the socio-psychological
characteristics of the heterogeneous population of Redditors.
Specifically, it contributes insight into the utility of a cooperative coevolutionary algorithm in constructing a model of
a diverse population. The rest of this paper proceeds as follows: prior related work is discussed in Section 2, along with
73
3.2
comparisons to the project presented here. Relevant technical background is given in Section 3. The experimental
approach is detailed in Section 4. The results of the experiments are given in Section 5, followed by a discussion of the
implications and directions for future work in Section 6.
2.
Coevolutionary Algorithms
A known weakness of traditional EAs is their poor performance on highly dimensional search spaces. Specifically,
they often fail on search spaces composed of many interacting subspaces [10]. Coevolutionary Algorithms (CEAs)
are special EAs that aim to overcome this weakness. They
are different from traditional EAs in that they calculate individuals’ fitness values based on their relationships with
other individuals in the population instead of considering
them independently. This leads to improved performance
on three problems types: 1) problems with arbitrarily large,
Cartesian-product search spaces, 2) problems with relative
or dynamic fitness measures, and 3) problems having complex structure [10]. These advantages make coevolution an
excellent approach for the problem considered in this paper:
evolving a heterogeneous population of interacting agents
(i.e., Redditors).
RELATED WORK
To the author’s knowledge, there have been no successful
attempts to model such a vast Internet community as Reddit. Van Miegham’s derivation of the Reddit Score was, in
fact, the first technical study of Reddit users. The research
presented here differs from Van Miegham’s Reddit Score in
that it seeks to replicate the behavior of Redditors instead
of simply analyzing it. In fact, it builds on Van Miegham’s
work by seeking a socio-psychological explanation for the
reportedly counter-intuitive Reddit Score trends.
Though Reddit hasn’t recieved much academic attention,
other social content-sharing sites have been the subject of
recent studies. Tang et al. performed a study of Digg that
was similar to Van Miegham’s analysis of Reddit [8]. The
goal of this study was to identify any unique characteristics
of Digg users (as opposed to users of other social aggregators), discern patterns of information spread, and study
the impact of individual social connections on general content dissemination. Tang et al. employed large-scale web
crawling techniques on 1.5 million Digg users and 10 million pieces of user-submitted content. The results suggested
three significant conclusions: 1) that Digg users behaved
heterogeneously when voting on content, 2) that voting behavior followed a power law degree distribution similar to
the distribution of Reddit scores, and 3) that voting behavior was linked to the age of Digg content.
CEAs are not applicable to all problem domains; in fact,
they often struggle or even fail where traditional EAs succeed. Such pathological behavior can be attributed to the
complexity introduced when individuals are allowed to interact with each other - the fitness landscape becomes dynamic
instead of remaining static.
There are two main groups of CEAs: competitive coevolutionary algorithms and cooperative coevolutionary algorithms. Historically speaking, competitive CEAs have been
more popular than their cooperative counterparts. Nonetheless, cooperative coevolution will be the focus of this paper,
as the relevance to the research objective is clear. For a
detailed account of competitive CEAs, see [5].
3.3
Both of these studies lay empirical foundations for the model
described in this report. The research presented here is
unique in that it seeks a predictive framework instead of
a descriptive one. Furthermore, there have not been any
approaches which have sought to capture the heterogeneous
nature of online populations. The prior studies of both Reddit and Digg have considered user behaviors as largely homogeneous.
Cooperative Coevolution
In cooperative coevolution, the individuals must work together to achieve some goal (or solve some problem). This
is in contrast with the ”arms race” that characterizes competitive coevolution. At each evaluation step, a subset of individuals are selected to be the collaborators in the problemsolving collaboration. Each collaborator contributes to the
problem-solving effort according to its designated role, and
then the collaboration as a whole is evaluated on its performance. Thus, it becomes meaningless to think of individuals
as having an intrinsic fitness value, as their success depends
on their interactions with other individuals.
3. BACKGROUND
3.1 Evolutionary Algorithms
Evolutionary Algorithms (EAs) are heuristic methods which
take inspiration from Darwinian evolution [3]. EAs are often used in optimization problems. Candidate solutions to
the target problem, called individuals, are encoded by genetic representations that are analogous to biological DNA.
Individuals are compared to each other via a fitness function that corresponds to the problem being solved. Thus,
the EA selects the most fit individuals to serve as parents
for the next generation of individuals. The creation of new
offspring from parents occurs via mutation (asexual) and
crossover (sexual), abstractions of mechanisms from biological evolution.
Typically, cooperative CEAs are applied to problems which
can be decomposed into components that can be independently solved. Then, each of many subpopulations is assigned a component to evolve a solution for. These solutions
are then put back together to form a solution to the global
problem. A general description of this process is given in
Algorithm 1.
3.4
Neuroevolution
Neuroevolution (NE) is the application of evolutionary computation to the search for optimal artificial neural networks.
Though recent work has focused on coevolving connection
weights alongside network structures, NE has long been used
to evolve connection weights for fixed topologies [6]. It has
also been successfully applied to competitive coevolution [7].
Though there are several specialized types of EAs, all share
emphases on survival of the fittest, heritable traits, and some
degree of stochasticity [3, 10]. The combination of these
traits make EAs powerful tools for exploring search spaces,
or sets of candidate solutions specific to some domain.
Neuroevolution, and the neural network representation in
74
for each population do
Initialize the population uniformly at random;
end
for each population do
Evaluate the population;
end
while the terminating condition is not met do
for each population do
Select parents from the population;
Generate offspring from the parents;
Select collaborators from the population;
Evaluate offspring with the collaborators;
Select survivors for the new population;
end
end
Algorithm 1: Generic Cooperative Coevolutionary Algorithm, from [10]
Figure 1: Individual ANN Architecture
take on a species-like relationship.
general, is an intuitive choice for the evolution of what is
essentially a decision system. For this experiment, a fixedtopology representation was chosen. The topology was intentially designed to disallow hidden neurons. When no
hidden neurons are present in the network, the input nodes
(which correspond to agent preferences) remain independent
from each other. Then, if we look at the network, we can see
exactly how each preference contributes to the final outcome.
This is instructive for our overarching goal of constructing
a socio-psychological model of heterogeneous Redditors.
4.
for each subpopulation in the population do
Randomly generate a parent;
Mutate the parent to generate 5 offspring;
end
Algorithm 2: Population Initialization
After the subpopulations are initialized, the competitive coevolution begins. During each round of coevolution, an initial collaboration is formed by randomly selecting one individual from each subpopulation. This gives a total of ten
individuals per collaboration, corresponding to distinct voting behaviors of ten Redditor archetypes. Each collaborator
evaluates the set of 30 pieces of content by setting its ANN
inputs according to the tags that are assigned to each piece
of content. If the tag is present, then the corresponding input is set to 1. Otherwise, it is set to 0. The age input
is also set according to the age of the content. After all
of the inputs have been set, the ANN is activated and its
output node is normalized. Querying the output node determines the individual’s voting behavior. If output < 0.25,
the content will be downvoted. If output > 0.75, it will be
upvoted. Otherwise, the Redditor will abstain from voting.
The voting process is summarized in Algorithm 3.
APPROACH
30 pieces of actual content were collected from Reddit. For
each piece of content, the following data were recorded: title,
number of upvotes, number of downvotes, total number of
upvotes minus downvotes, age (in hours), and ranking. The
comments associated with each piece of content were also
examined. The contents of these comments, along with the
format of each piece of content (image, video, gif, etc.), were
used to generate between 3 and 6 tags for each piece of
content. These tags were manually specified by the author
and amounted to 65 possible tags. The same tag could be
applied to multiple pieces of content. A full list of tags used
in this implementation is given in Appendix A.
for each piece of content to be evaluated do
for each of the 10 collaborators do
Reset the collaborator’s ANN to 0’s;
for each tag on the piece of content do
The corresponding ANN input node ← 1;
end
Activate the ANN;
Query the ANN’s output node;
Normalize the output value;
if normalized output > 0.75 then
Upvote the content;
end
else if normalized output < 0.25 then
Downvote the content;
end
end
end
Algorithm 3: Mechanism for voting on content
Individual Redditors were represented as artificial neural
networks (ANNs) using the NEAT genome structure [6].
Each ANN had 65 input nodes corresponding to the 65 possible tags that could be assigned to a piece of content. Additionally, a 66th input node corresponded to the age of the
content. There was also a single bias node. All input nodes
were directly connected to the single output node, which determined the voting behavior of the modeled Redditor. All
nodes in the ANN have linear activation functions, and the
input nodes all have their values normalized to (0,1). The
ANN architecture is shown in Figure 1.
Individual Redditors were grouped into 10 subpopulations
consisting of 5 individuals each, giving a total of 50 individuals in the population-at-large. The process for initializing
these subpopulations at the beginning of the experiments is
described in Algorithm 2. Because all of the individuals in a
subpopulation are offspring of a single parent, they naturally
75
Once every collaborator has voted on all of the content, the
collaboration’s votes are summed to get a popularity value
for each piece of content:
P opularity = Σ(upvotes) − Σ(downvotes)
Initialize population;
while no coalition has met the fitness threshold do
Randomly select one member of each population to
serve in the collaboration;
for each of the 10 populations do
for each of the 5 members of that population do
Include the member as part of the collaboration;
Evaluate the fitness of the collaboration;
end
Select the population member that contributes the
most fitness;
Delete the other population members;
Replace them with offspring of the most-fit member;
end
end
Algorithm 5: Implemented Cooperative Coevolutionary
Algorithm
(1)
The pieces of content are then sorted according to their popularity values and assigned a corresponding ranking. This
collectively-decided ranking is compared to the ranking from
actual Redditors to determine the collaboration’s fitness.
The mechanism for determining collaborative fitness is described in Algorithm 4.
for each piece of content do
if the content wasn’t ranked first then
Get the content ranked above this content;
if the two pieces of content are correctly ordered by
the collaboration then
fitness ← fitness+1;
end
end
if the content wasn’t ranked last then
Get the content ranked below this content;
if the two pieces of content are correctly ordered by
the collaboration then
fitness ← fitness+1;
end
end
end
Algorithm 4: Mechanism for calculating fitness of a collaboration
it was unable to exceed a fitness of 2. In every test, fitness
values of 1 or 2 were found within the first 5 generations. It
is expected that fitness values of 1 and 2 would occur with
the same frequency - if story A is correctly ordered next to
story B, then story B is also correctly ordered next to story
A. So, this result validates at least one aspect of the fitness
function. However, it is unclear why nonzero fitness values
would appear so quickly, but would not exceed 2. Such
a result implies that the search happened to start off in a
fortunate location on the search space every time. While this
is not impossible, there may be an alternate explanation for
this behavior that does not rely on coincidence. As discussed
in the following section, future work will test hypotheses
about the causes of the failed convergence.
6.
This collaborative fitness is used to decide which individuals
will survive through the next generation. At each iteration,
the algorithm randomly selects one member of each subpopulation to serve in the collaboration. Then, it holds 9 of the
10 collaborators constant while testing the individual fitness of the final collaborator. In the context of cooperative
coevolution, individual fitness is simply an individual’s aptitude for contributing to a collaboration. So, the algorithm
switches that final collaborator out with the other members of its subpopulation to see which one gives the highest
collaborative fitness. The highest-performing individual is
chosen as the parent for the subpopulation, and the other
individuals are replaced with its offspring. The offspring are
generated using mutation of the connection weights. The
mutation weights were varied from 0.01 to 0.5. The coevolutionary process is summarized in Algorithm 5.
As mentioned in Section 3, cooperative coevolution is not
well-understood; competitive coevolution has been the subject of substantially more analysis. Two widely-touted advantages of cooperative CEAs are their ability to handle interacting search spaces and their ability to handle infinitely
large spaces. However, these claims may not hold in all domains. Furthermore, there is no guarantee that the solution
will be found in a reasonable amount of time.
The algorithm was run with gradually increasing fitness thresholds. Initially, the algorithm was set to terminate after
reaching a fitness of 0. This strengthens the claim that the
fitness function works as intended. The fitness threshold
was then increased by 1 for each experiment until the algorithm either reached the maximum fitness (58) or failed to
converge on a solution.
5.
DISCUSSION
The goal of this experiment was to test whether or not a cooperative coevolutionary algorithm could find a valid model
of heterogeneous Reddit users. The results show that the
simple modeling approach outlined in this paper was not
sufficient. This section focuses on potential explanations for
this insufficiency and outlines methods for testing these explanations.
RESULTS
The implemented cooperative coevolutionary algorithm was
unable to reach the maximum fitness value of 58. In fact,
76
The most significant obstacle to this goal is the dimensionality of the search space: the domain described in this paper
consisted of 10 interacting individuals with 65 connection
weights each to optimize. Such a search space is a far cry
from the canonical ”toy” problems such as maximizing the
number of 1’s in a binary string. In this way, the search
space was a more accurate model of real-world problems
than many other experiments reported in academic literature. This realization motivates a much-needed direction for
future research: How can we create heuristic methods which
are capable of searching arbitrarily rich spaces? The results
reported here suggest that our current best methods may
not be enough.
Peter Kollock and Marc Smith, editors, Communities
and Cyberspace. Routledge, New York, 1999.
[10] R. Paul Wiegand. An Analysis of Cooperative
Coevolutionary Algorithms. PhD thesis, George Mason
University, 2003.
The model could also be improved by a more robust tagging
mechanism. The 30 pieces of content used for evaluation
in this project generated 65 unique tags. Additional tags
were intentionally excluded by the author in the interest
of keeping the model’s dimensionality as low as reasonably
possible. However, the salient point isn’t the number of
tags, but the way in which they were selected - manually,
by a human. For an arbitrarily large dataset, it would be
impossible for a human to evaluate each and every piece of
content. Thus, an automated tagging algorithm would allow
experiments to be undertaken on a larger scale.
APPENDIX
A. LIST OF CONTENT TAGS
video, engineering, foreign, war, humanitarian, image, camping, handmade, funny, worldnews, education, psychology,
politics, liberal, gaming, skyrim, animal, Africa, nature,
politics, technology, phones, patents, rare, Europe, ruins,
comic, lonely, todayilearned, chess, trivia, language, science, globalwarming, economics, tattoos, unfortunate, historical, wordplay, AdviceAnimals, film, Twilight, wordplay,
reddit, happy, success, writing, innuendo, gif, kids, crude,
twinkies, guns, pizza, heroic, wtf, road, nonsensical, worldnews, America, celebrity, AskReddit, christmas, gender, facebook
On a related note, it is critical that these experiments are,
in fact, undertaken on a larger scale. This experiment considered a dataset consisting of the top 30 stories on an arbitrarily chosen day. In contrast, approximately 127,000,000
stories are submitted to Reddit every day. The results of
an experiment with such a comparatively small dataset may
not scale to the level of Reddit’s actual load.
Though the results of this experiment were not the results
that were anticipated, this does not mean that the research
was all for naught. Even though the algorithm failed to
converge to a solution, we can still glean insights into the
limits of the cooperative coevolutionary approach. Such insights are the most significant contribution of this work. If
we only undertake simple endeavors that we know will succeed, we will never truly know what is possible from what
is impossible.
7.
REFERENCES
[1] Michael S. Bernstein, Andres Monroy-Hernandez,
Drew Harry, Paul Andre, Katrina Panovich, and Greg
Vargas. 4chan and \b\: An analysis of anonymity and
ephemerality in a large online community. In
Proceedings of the 5th International AAAI Conference
on Weblogs and Social Media. AAAI, 2011.
[2] Emile Durkheim. The Division of Labor in Society.
Free Press, New York, 1997. Trans. Lewis A Coser.
[3] Kenneth A. De Jong. Evolutionary Computation. MIT
Press, 2006.
[4] Piet Van Miegham. Human psychology of common
appraisal: The reddit score. IEEE Transactions on
Multimedia, 13(6):1404–1406, 2011.
[5] Christopher D. Rosin and Richard K. Belew. New
methods for competitive coevolution. Evolutionary
Computation, 5, 1997. MIT Press.
[6] Kenneth O. Stanley and Risto Miikkulainen. Evolving
neural networks through augmenting topologies.
[7] Kenneth O. Stanley and Risto Miikkulainen.
Competitive coevolution through evolutionary
complexification. Journal of Artificial Intelligence
Research, 21:63–100, 2004.
[8] Siyu Tang, Norbert Blenn, Christian Doerr, and
Piet Van Miegham. Digging in the digg social news
website. IEEE Transactions on Multimedia,
15(6):1163–1175, 2011.
[9] Barry Wellman and Milena Gulia. Net surfers don’t
ride alone: Virtual communities as communities. In
77
An implementation of CHALMS (Coupled Housing and
Land Market Simulator)
Michael Gabilondo
ABSTRACT
are other existing models the deal with housing markets or
land markets [3] [6] [2]. However, none of these simulations
consider both a coupled land and housing market and microeconomic decision making. The CHALMS model is novel
in this sense.
This paper describes an independent implementation of a
coupled housing and land market simulator (CHALMS); the
system was originally described in [5] [4]. CHALMS is a spatially explicit agent-based economic simulator, where each of
the agents is behaves in a self-interested, optimizing way to
maximize their profits or utility. The spatial setting is a suburban community on the urban fringe, with a small amount
of houses initially present and the rest of the land occupied
by farms. There are three types of agents: one developer,
consumers, and farmers. The population of consumers grows
exogenously and seeks to buy houses to maximize their utility. The developer buys land from farmers to build houses
to sell to consumers to maximize the expected profit. The
farmers decide whether to sell their land to the developer or
continue farming.
The paper is organized as follows. Section 2 gives an overview
of the agents in the model. Section 3 gives a sense of the
sequence of events per time step. Section 4 describes our
experimental setup. Section 5 describes our experimental
results. Section 6 concludes.
2. MODEL: OVERVIEW OF AGENTS
2.1 Consumers
The consumers in the model seek to buy houses by maximizing a utility function that incorprates the consumer’s
incomes, the consumer’s house size and lot size preferences,
the consumer’s proportion of income devoted to housing, the
developer’s asking price (rent), and the travel cost from the
house to the SDD. The Cobb-Douglas utility function for
consumers is shown in Equation 1.
We show that our implementation of the CHALMS system
achieves development patterns that are comparable to the
patterns described in the original paper. There are also
some discrpencies between our model and the original model,
which are likely due for two reasons: (1) the simplified price
expectation models of the agents in our implementation; and
(2) the memory restrictions in our experimental platform
that caused our implementation to run for nine simulated
years instead of twenty as in the original experiments.
U (c, n) = (Ic − Pask (n) − ψn )αc hn βc ln γc
In the equation above, n is the house in the housing market,
c is the consumer, Ic is the income of consumer c, Pask (n)
is the developer’s asking price (rent) for house n, ψn is the
travel cost from house n to the SDD, αc is consumer’s proportion of income devoted to housing, βc is the consumer’s
value for lot sizes and γc is the consumer’s value for house
sizes. At the initial state, Pask (n) has not been computed
by the developer, so this value is initialized to Ic − Ic αc .
Keywords
Agent-based computational economics, Land markets, Housing markets, Coupled markets, Housing density
1.
(1)
BACKGROUND
Previous work has argued that agent-based economic models
can be useful way of studying economics since such models
have advantages over traditional spatial equilibrium models
[1]. In this work we investigate a coupled land and housing
market by agent-base simulation. We have implemented the
CHALMS model described in previous work [5] [4]. There
The Willingness to Pay (WTP) of a consumer c is equal to
“the portion of the consumer’s income he is willing to pay for
housing as given by the Cobb-Douglas structure” [5], shown
in Equation 2.
W T P (c, n) = (Ic − ψn )(βc + γc )
(2)
The consumer calculates the rent he is willing to pay for a
house, R∗ , which represents, “an optimal rent such that the
consumer would be indifferent among housing options,” and
is given in Equation 3.
78
2.2
R∗ (c, n) = Ic − ψn −
∗
U
hn βc ln γc
1
αc
(3)
In the equation above, U ∗ represents the maximum utility
among all housing options on the market.
The developer must first predict the number of consumers
that will bid in the current period, since the exogenous population growth rate is not known to the developer. The
number of predicted bidders equals the number of bidders
who did not acquire houses in the previous period plus the
predicted number of new bidders. In our model we make
the simplifying assumption that the developer predicts 10%
new bidders; this differs from the original work, which uses
prediction models to calculate the number of new bidders
[5]. These population expectation models extrapolate from
past growth trends and are similar to the developer’s price
expectation models, described in the paragraph below.
The Willingness to Bid (WTB) of a consumer c is formed by
taking the difference between the developer’s asking price
and optimal rent and subtracting this difference from the
consumer’s WTP, and is given in Equation 4.
W T B(c, n) = W T P (c, n) − (Pask (n) − R∗ (c, n))
(4)
The set of houses on which consumer c actually bids is given
by the set H(c),
H(c) = {h : W T B(c, h) ≥ Pask (h)Ωlt }
At the beginning of each time step, the developer has the
rents for each constructed house from previous periods. From
this, he calculates an expected rent for each constructed
house for the current time period. In the original CHALMS
model, the developer has a set of 20 models which he uses
to calculate the expected rent using the history of rents for
each house; the active model is that which was most accurate in predicting the expected rent in the previous period
[5]. In our model, the developer’s expected rent for a house
is simply the rent of that house from the last period, which
corresponds to one of the possible models in the original
work.
(5)
In equation 5 above, h is a house on the housing market,
and Ωlt is the bid level for housing lot size (l) and house
size (t) combination, and is defined as the ratio between the
number bids for houses of type lt that have been above the
seller’s asking price and the number of bids for that housing
type that have been below the asking price in the past.
The housing market competition (HM Cc ) that consumer c
faces is defined as,
HM C(c) =
NC − NH
NC + NH
The Developer
The developer buys land from farmers to build houses to sell
to consumers to maximize the expected profit (i.e., minimize
the expected loss).
Once the expected rents are calculated for existing houses,
the developer calculates projected rents for each possible
housing type on each acre of farmland owned by farmers.
The developer uses one of three methods to calculate the
projected rent for each housing type on each undeveloped
cell.
(6)
In equation 6 above, N H is the number of houses in H(c)
and N C is the number of other consumers bidding for the
same houses in H(c).
1. If the housing type exists within a distance of nclose =
10 cells away from the undeveloped cell, then the projected rent involves a combination of local rent information for that housing type and global rent information for that housing type, shown in Equation 8 below.
If HM C(c) is only slightly positive or negative, then consumer c faces low competition in the housing market. This
can happen if more expensive homes are introduced; only the
wealthiest of consumers will bid on those expensive houses.
In these cases, consumers do not scale up their bids as much
above the optimal rent.
loc
reg
Rproj = 0.3Rproj
(i, lt) + 0.7Rproj
(i, lt)
(8)
The undeveloped cell is given by i and the housing
loc
type is given by lt. The local component, Rproj
(i, lt),
is defined as
However, if HM C(c) is large, the consumer c faces high
competition in the housing market. This can happen, for
example, if many low income consumers are bidding for affordable low-density housing near the initial development.
In these caess, consumers scale up their bids above their optimal rent to increase their likelihood of being the highest
bidder, which in turn raises the prices of those houses so
they become less affordable.
loc
loc
Rproj
(i, lt) = Rlt
− mcDloc (i, lt)
(9)
loc
where Rlt
is the average rent for housing type lt within
the nclose closest cells, where the rents are weighted by
their distance from the SDD; mc is the travel cost per
cell and Dloc (i, lt) is the distance from cell i to the
closest developed cell with housing type lt.
The bid that consumer c places on house h is given by Equation 7 below.
reg
The global component, Rproj
(i, lt), is defined as
Pbid (c, h) = R∗ (c, h) + HM Cc [W T P (c, h) − Pask (h)] (7)
reg
reg
reg
(i, lt) = Rlt
− mc(Di − Dlt
)
Rproj
79
(10)
reg
where Rlt
is the global average rent for housing type
reg
lt, Di is the distance from cell i to the SDD, and Dlt
is the average distance from all houses of type lt to the
SDD.
The W T P (F, t) is simply the sum of the best projected rents
over all cells of farm F divided by the total number of cells
in farm F .
2. If the housing type does not exist within the nclose
closest cells but exists somewhere in the landscape,
then the projected rent is simply the global component
reg
Rproj
(i, lt) given by Equation 10.
2.3
3. If the housing type does not exist anywhere in the
landscape, then the projected rent is calculated using local and global information about consumer utilities. In this case, the rent projection is given by Equation 8 above, where the local and global components,
reg
loc
Rproj
(i, lt) and Rproj
(i, lt), respectively, are subsituted
by the two equations below. These equations have the
same form as the consumer’s optimal rent function,
loc
R∗ . The local component Rproj
(i, lt) is given by
loc
Rproj
(i, lt)
=
Inloc
− ψi −
Unloc
hβc lγc
α1
The farmer also forms an expectation of what the farm is
worth on the market based on the closing prices of other
farms. The farmer observes the farm closing prices (if any)
from the last period, and discounts the average observed
prices based on the number of cells away his farm is located.
We assume a simplified model for spatial discounting, and
consider that each cell that his farm is away from the sold
farms reduces the his spatially discounted price by $15000;
the original work uses a learning algorithm to determine
the discount per cell [5]. The farmer takes this spatially
discounted price as the expected market value of his farm in
the previous period.
c
(11)
where Inloc is the average income of houses located
within the n = nclose closest cells, Unloc is the average
utility of houses located within the n = nclose closest
cells, and ψi is the travel cost from cell i to the SDD.
The farmer then computes the expected market value of his
farm at the current time period by using a price expectation
model. In the original work, the farmer has a set of 20
price expectation models similar to the developer, described
above. However, we have made the simplfying assumption
that the spatially discounted expected market price for the
farm this period equals the spatially discounted price in the
last period.
reg
The global component, Rproj
(i, lt), is given by,
reg
Rproj
(i, lt) = Inreg − ψi −
U reg
hβ l γ
1
Farmers
Farmers decide whether to sell their land to the developer or
continue farming. A farmer will not sell the farm to the developer if the developer’s WTP for the farm does not exceed
the return from farming, which is the agricultural return per
cell (given in Table 2) multiplied by the number of cells in
the farm, and is denoted Vagr .
α
(12)
where Inreg is the global average income, U reg is the
global average utility, and α, β and γ are the averages
of those values over the entire landscape.
The spatially discounted in the current period for cell i of
farm F is denoted PLproj (Fi ), and the expected agricultural
return for cell i of farm F is denoted Vagr (Fi ). The Willingness to Accept (WTA) for farm cell i of farm F at time t is
given by
After calculating the projected rent for each housing type on
each undeveloped cell, the developer calculates the projected
return for each housing type on each undeveloped cell. The
projected return for cell i and housing type lt is given as
Return(i, lt) in the equation below.
W T A(Fi , t) = max(PLproj (Fi ), Vagr (Fi ))
(15)
(13)
The WTA for the entire farm is simply the sum of the WTA
for each cell of the farm.
Above, BC is the building cost, IC is the infrastructure cost
for housing type lt (given in Table 2), LP is the price of land
for lot size l based on the current price of land for the farm
cell and Rproj is the projected rent calculated by one of the
three methods above.
The developer will bid on all farms for which is WTP is
greater than the farmer’s WTA. The developer forms a bid
price, PbidL (Fi , t), from his initial WTP, while the farmer
forms an asking price, PaskL (Fi , t), from his initial WTA.
The asking price and bidding price are formed by adjustments to the WTA and WTP based on land market competition, ǫ, and is called the bargaining power of the land
market.
Return(i, lt) = Rproj (i, lt) − BC − IC − LP
The projected rent associated with with cell i that produces
the maximum return is denoted Rmax (i). The developer
forms a Willingness to Pay (WTP) for farm F at time t,
given by Equation below.
W T P (F, t) =
P
j∈Fi
Rmax (j)
AF
The bargaining power represents the difference between the
amount of land that is demanded by the developer (which is
based on the number of predicted bidding consumers) and
the amount of land on the market (for which WTP > WTA).
The bargaining power ǫ is defined as
(14)
80
3.1
New arrivals and vacancies
The first event in each time step is that the consumer population grows by the exogenous population growth rate. These
represent new consumers seeking to move into the suburbs
and entering the housing market. Also, consumers’ residence
time expires; these consumers move out of their houses and
re-enter the housing market. Both of these parameters are
given in Table 2.
3.2
Developer markets houses
The developer then markets houses to consumers. This involves predicting the number of bidders, determining the
best housing types to construct on land owned by farmers,
buying land from farmers, and building houses. All of these
steps are described in the sections above.
3.3
Consumers buy houses
Finally, the consumers determine each house to bid on. Each
consumer determines the housing market of houses he is allowed to bid on and places his bid, as described above.
It is possible a consumer has the highest bid for more than
one house. To this end, a process for matching winning
consumers to houses is executed. Consumers having at least
one winning bid are identified and are placed into a set of
winning bidders. For each consumer in the set of winning
bidders, the set of houses for which he has the highest bid is
identified. For each of those houses, the consumer’s utility
is recalculated using the winning bid instead of the initial
asking price. The house with the highest utility is chosen as
the consumer’s new residence and the rent for that period
is set to the winning bid. Both the consumer and the house
are removed from the market and the process is reiterated
until there are no consumers, no more positive bids, or no
more houses.
Figure 1: This figure shows the main sequence of
events that occurs in each time step.
ǫ=
dland − AF ∗
dland + AF ∗
(16)
where dland is the number of acres demanded by the developer and AF ∗ is the number of acres of land on the market.
4.
The farmer’s asking price for cell i of farm F is given by
PaskL (Fi , t) = max(W T A(Fi , t) ∗ (1 + ǫ), Vagr (Fi ))
The simulated landscape is 80 cells by 80 cells where each
cell represents 1 acre (6400 acres). Initially there are 334
houses near the SDD and the rest of the area is farmland;
there are 42 initial farms.
(17)
The developer’s bid price for cell i of farm F is given by
In our experiments, were simulated only nine years instead
of the full twenty as in the original work due to memory limitations on our experimental system. The average behavior
of the model was taken over 5 runs instead of 30 runs, as in
the original work, due to time limitations.
PbidL (Fi , t) = min(W T P (Fi , t) ∗ (1 + ǫ), W T P (Fi , t)) (18)
Positive bargaining power implies that the developer demands more land than farmers supply, so farmer asks more
than WTA. Negative bargaining power implies that farmers
supply more land than the developer demands, so developer
will bid below his WTP.
3.
EXPERIMENTAL SETUP
The initial condititions represent the state of the model before the first time step begins, and a summary is shown in
Table 2 below.
5.
EXPERIMENTAL RESULTS
Although we have made some simplifying assumptions in our
model and although we simulated fewer years, our results are
comparable with the original work.
MODEL: A SEQUENTIAL VIEW
Figure 10 shows the simulated landscape at the end of year
nine for each of the five runs. The mosaic grayscale pattern represents unpurchased farmland, while the black areas
represent developer-owned land that does not have houses.
We describe the model in terms of the sequence of events
that occurs in each time step; an overview is shown in Figure
3.
81
Mean (Std. dev) farm size in acres
Mean (Std. dev) agricultural return in $/acre
Building cost per square foot
Infrastructure cost per housing unit
0.25 acre lots
0.50 acre lots
1.00 acre lots
2.00 acre lots
5.00 acre lots
10.00 acre lots
Household income classes in $1000s
Low income
Middle income
High income
Household income distribution mean (std. dev)
Share of income on housing expenditure (α)
Low income
Middle income
High income
Consumer house (β) and lot (γ) preferences
Transportation costs in $/mile
Exogenous rate of population growth
Consumer residence time mean (std. dev)
Number of initial houses present
Number of initial farms present
128 (71)
2486 (249)
$125
$10000
$15000
$20000
$23000
$30000
$40000
40-59
60-99
100-200
86 (39)
Figure 4: This plot shows the average lot size of
houses built in each zone at the end of year nine.
Zone i represents cells that are between 5*i and
5*(i+1) - 1 cells away from the SDD. For example,
Zone 2 represents cells that are between 10 and 14
cells away from the SDD. The averages were computed from a sample of five runs.
.35-.42
.27-.34
.18-.26
α=β+γ
1.84
10%
6.2 (5.5)
334
42
Figure 2: Parameter settings for the initial conditions
Lot Size
0.25
0.25
0.25
0.50
0.50
0.50
1.00
1.00
1.00
2.00
2.00
2.00
House Size
1500
2000
2500
1500
2000
2500
1500
2000
2500
1500
2000
2500
Avg # lots C.I.
(25.28, 911.12)
(8.96, 15.84)
(4.17, 5.03)
(153.87, 1168.53)
(53.03, 70.57)
(10.85, 15.15)
(32.00, 1302.40)
(58.85, 64.35)
(29.05, 39.35)
(6.01, 95.59)
(16.35, 26.85)
(64.92, 94.28)
Avg rent ($1k) CI
(89.57, 237.27)
(77.83, 181.40)
(101.26, 219.74)
(77.38, 180.69)
(101.09, 254.09)
(78.03, 217.89)
(77.21, 312.97)
(99.40, 249.21)
(114.02, 268.31)
(128.33, 273.63)
(89.14, 227.47)
(120.86, 242.66)
Figure 5: This plot shows the average farm price
per cell of farms residing in each zone at any time
step. Zone i represents cells that are between 5*i
and 5*(i+1) - 1 cells away from the SDD. The averages were computed from a sample of five runs.
Figure 3: This table shows, for each housing type,
the 95% confidence interval for the average number
of lots and the average rent at the end of year nine.
The averages were computed from a sample of five
runs. No five or ten acre lots were built in any of
the runs. Lot size is in acres and house size is in
square feet.
The other solid gray regions represent housing lots containing various housing types (distinctions are not possible in
grayscale). The SDD is shown in the top center part of the
landscape.
There are three distinct development patterns that show up.
The landscape on row 2, column 2 shows a scenario where
the developer never purchased any farms, i.e., the developer never bid more for a farm than the farm’s base agri-
Figure 6: This plot shows the average farm price per
cell of farms in each time step. The averages were
computed from a sample of five runs.
82
Figure 7: This plot shows the average housing rent
per house in each time step. The averages were
computed from a sample of five runs.
Figure 10: This figure shows the simulated landscape at the end of year nine for each of the five
runs.
Figure 8: This plot shows a comparison of the average number of lots and the average number of
housing acres developed over time. The number
of lots increases faster than the number of housing
acres, which represents an increasing concentration
of many small lots per housing acre. The averages
were computed from a sample of five runs and the
confidence intervals are not shown.
cultural value. This means that the increased rents near
the SDD (which are caused by consumers vacating and new
consumers moving in) never caused the developer to increase
the farm bids enough to exceed the farmers’ expected agricultural value.
The lanscapes on row 1, column 1, and on row 1, column 2
show similar development patterns. In both cases, the developer purchased farmland near the existing construction. As
the developer-owned land becomes populated with houses,
the nearby farmland increases in value since the developer
has higher projected rents for those areas. This causes the
developer to purchase land near the existing construction.
In both these cases, prevailing lot sizes are 0.25, 0.5 and 1.0
acres, while 2.0 acre lots are rare or nonexistant.
The landscapes on row 1, column 2, and on row 3, column
1 show similar development patterns that are distinct from
the cases above. In both cases, the initial purchased farms
near the SDD contains either 0.5 acre lots of 1.0 acre lots.
However, the additional farms purhcased by the developer
were distant from the existing development. By the end of
year nine, most of the distant farms have not been populated
with houses, but contain a few 2.0 acre lots. This scenario
occurs because the initial farms which were purchased by the
developer were purchased at high cost, which caused nearby
farmers to increase their asking prices, while distant farmers
increased their asking prices less due to spatial discounting.
Figure 9: This plot shows the average rent of houses
built in each zone at any time step. Zone i represents
cells that are between 5*i and 5*(i+1) - 1 cells away
from the SDD. For example, Zone 2 represents cells
that are between 10 and 14 cells away from the SDD.
The averages were computed from a sample of five
runs.
83
6.
CONCLUSION
We have implemented the CHALMS model described in [5]
[4]. We have made some simplfying assumptions in our
model as well as simulating fewer development years due to
memory limitations. However, our results indicate that similar development patterns emerge nonetheless. This work
demonstrates that an independent implementation of the
CHALMS achieves comparable results even though some differences between the models exist.
7.
REFERENCES
[1] W. B. Arthur. Chapter 32 out-of-equilibrium economics
and agent-based modeling. volume 2 of Handbook of
Computational Economics, pages 1551 – 1564. Elsevier,
2006.
[2] D. Ettema. A multi-agent model of urban processes:
Modelling relocation processes and price setting in
housing markets. Computers, Environment and Urban
Systems, 35(1):1 – 11, 2011.
[3] T. Filatova, D. Parker, and A. V. van der. Agent-based
urban land markets: Agent’s pricing behavior, land
prices and urban land use change. Journal of Artificial
Societies and Social Simulation, 12(1), 2009.
[4] N. Magliocca, V. McConnell, M. Walls, and E. Safirova.
Zoning on the urban fringe: Results from a new
approach to modeling land and housing markets.
Regional Science and Urban Economics, 42(1âĂŞ2):198
– 210, 2012.
[5] N. Magliocca, E. Safirova, V. McConnell, and M. Walls.
An economic agent-based model of coupled housing and
land markets (chalms). Computers, Environment and
Urban Systems, 35(3):183 – 191, 2011.
[6] D. T. Robinson and D. G. Brown. Evaluating the effects
of landâĂŘuse development policies on exâĂŘurban
forest cover: An integrated agentâĂŘbased gis
approach. International Journal of Geographical
Information Science, 23(9):1211–1232, 2009.
84
Power Vacuum after Disasters:
Cooperating Gangs and their effect on Social Recovery
Miguel A. Becerra
University of Central Florida
4000 Central Florida Blvd.
Orlando, FL., 32816
miguelb@knights.ucf.edu
an example of fear and confusion escalating to anarchy and social
chaos.
ABSTRACT
Disasters are terrible tragedies that affect a society’s morale,
descending from a lawful to anarchic state. What can be seen in
recent disasters and in history, when a major power is removed, it
creates a power vacuum that allows previous powerless
individuals to create formidable forces; people will group up for
safety based on whether group support is likely or not. In a
society where police power is severely crippled and the
population has limited information of society’s current state, these
forces may impede post-disaster relief efforts. In this paper, we
will expand the Epstein’s and Salgado’s team’s work to
implement the idea of disaster-created gangs and observe their
effect on the society’s ability to return to near pre-disaster
conditions.
2. Related Information
2.1 Background
When such events happen, post-disaster relief efforts must
coordinate with a law enforcement force to return law into the
land so they may begin to repair much of the damage and return to
near or better pre-disaster conditions. Many models exist
demonstrating their strength of modeling, simulating and
predicting social behavior in many situations. One such model is
Joshua Epstein’s Civil Violence agent-based model, expanded
from his previous work with Robert Axtell surveying
implementations of agent-based computation to analyze and
model micro- and macrocosms of people [1]. The Civil Violence
model was a rudimentary representation of civilian agents, acting
as the general population, and cops, acting as law enforcement for
the society. The civilian agents would have several variables, an
example of them would be their perceived hardship and
legitimacy of the government; based on these values, along with
several equations acting as other underlying factors determining
these views, and their personal threshold, a person would actively
rebel against the local government, otherwise, they would remain
quiet. The cops, on the other hand, would patrol and arrest any
actively rebelling civilians that enter its view [2]. It is this
powerful technique and view of modeling heterogeneous agents
on a local level as well as the emergent behavior of the system
that has led many papers using this as a basis for similar
scenarios, such as drinking behavior, and more distant studies,
such as molecular organization.
Categories and Subject Descriptors
I.6.4 [Simulation and Modeling]:
Analysis
Model Validation and
General Terms
Algorithms, Measurement, experimentation, Security, Human
factors, Theory.
Keywords
Agent-based Modeling, Deviant Behavior, Escalation, Disasters,
Mob Mentality, Netlogo, Rebellion, Cooperation.
1. INTRODUCTION
Natural events test a society’s implementation of safety
regulations and safeguards to protect their people; time and time
again, these safeguards survive each test as well as the day-to-day
wear and tear. However, there are times in which these
implementations deteriorate to an inadequate point or, worse, are
insufficient to combat every foreseeable force. An infamous
example of such an event happened during Hurricane Katrina in
which the wind force and rampaging water broke through the
levees and other defenses, creating billions of dollars in damage
and many lives loss, all of which could have been preventable.
The prevention of such inadequacies, however, is not the purpose
of this paper; instead, we are discussing what happens afterwards.
One such paper that does this is one by Salgado, Marchione, and
Gill with their extension of Epstein’s model; their design would
attempt to model the anarchy and looting that occurs after a
disaster, using the agents’ view as a metaphor for the information,
or lack of, to simulate such chaos and confusion [3]. The main
premise of their paper is that, in such a disastrous scenario, an
individual would stop their law-abiding behavior and begin a
lookout for precious resources scattered around the world; this
change in behavior is ultimately governed by the knowledge of
how scarce resources become, take much higher risks as resources
become more limited than when the disaster started. Through
these concepts, they experimented with influence of the police’
and citizens’ information on relief efforts to return the society to
near pre-disaster conditions. The results proved that, while
expanding the information available to the police or citizens had
their positive and negative effects, particularly when these
implementations are enacted, the best outcome would of a joint
strategy: reinforcing the police force and keeping the citizens
After Hurricane Katrina devastated the area, most, if not all, lines
of communication were lost, millions of homes were without
clean water and electricity, millions more were displaced, and
essentially no one had a handle on the situation. From this
desperate situation, many groups of people were forced to escalate
their behavior to survive - interviews with eyewitnesses tell tales
of desperation: neighbor versus neighbor fighting for supplies and
items, looting local stores, and some having to use deadly force to
protect themselves or to exert power over others. This, indeed, is
85
Because we are unable to validate the model, we do, however,
hope that by using strong and established models [2][5] as a
foundation for the experiment, we can draw theoretical
implications reinforced by these strategies. Such interpretation can
be credible as: (1) Model has general features of protest, and (2)
Group Identity is a key factor for group behavior, two strengths
that has been proven in various models and that will be present in
the design of the experiment.
apprised of the situation, creating an environment to accelerate
efforts. This model would be most advantageous for first
responders to calculate the necessary initial law enforcement force
to be inserted into the disaster zone as well as to construct ideas
and strategies based on a population.
2.2 Assumptions
While these two papers have shown much strength, it would be
necessary to further the idea by adding several assumptions based
on what has been known to occur in these situations. First, we
must establish the two assumptions that act as the basis for
Salgado’s team’s paper, then, we will discuss the additional
assumptions for post-disaster group creation.
3. Experimental Model
As it is using Epstein’s design as a foundation, we will be using
an Agent-Based Model, expanded by the assumptions previously
discussed. This section will explain the concepts and formulas that
will be dictating the behavior of these agents within the system.
2.2.1 Assumption 1
There will be two agent types interacting with the system:
Civilians and Law Enforcement. Aside from being interacting
agents, they are dissimilar in every way but one: each agent has a
value containing v, the visibility radius of each individual agent;
this value will be used to determine the neighborhood, the area in
which the agent will be attempting to view other civilians and
police as well as resources.
Disasters increase the perceived benefits and decrease the
perceived costs individuals expect to obtain from their
participation from looting. [3]
When a disaster occurs, the citizens within the disaster zone will
experience a diminished view of the information that exists
around them. Because this is something that will affect the
transmission of information for citizens and law enforcement
alike, the general population that was once law-abiding will begin
view their costs from punishment to decrease, increasing the
benefits of being an unlawful individual. Additionally, due to the
limited resources that now exist, these once generally available
items, such as food and water, now become of higher value; this
obviously increases an individual’s desire to commit previously
greatly punishable acts.
3.1 World Initialization
The world must be prepared prior to the introduction of the
Civilians and Law Enforcement. Each patch will contain a view of
the initial neighborhood the agents will be using to examine and
evaluate their current state and what actions they will take;
additionally, we need to not only prepare for the agents but also
prepare for the initialization of the resources civilians will be
competing for. Each patch is required to hold the neighborhood as
well as storing the quantity of resources; these patches that are
holding such items are a metaphor for the real-life stores and
storage facilities, areas of importance. Afterwards, based on the
initial resource density established by the user, there needs to be a
distribution of the resources. Each patch that will be holding
resources will then be arranged to store the arbitrary amount of 30
units.
2.2.2 Assumption 2
Disasters reduce the amount and quality of the information
individuals perceive from their environment.
There is a loss of information that occurs on those within the
affected area. Prior to the disaster, television, phones and the
internet have proved to be a vital resource to understand and see a
much grander distance; when these outlets are lost, they are a lack
of confidence of what lies farther away as the only information an
individual can trust is what they are able to see within their field
of vision. Because of this sudden loss, this can cause confusion to
the individuals, further distorting their limited view.
Now, the system can begin to randomly distribute the cops and
agents, once again based on the initial user-defined density values.
What is unique to the civilians is the concept of their home. While
resources exist as storage facilities and stores, the patches where
the civilians spawn will be representing the civilian’s home. It is
important for civilians to know where their homes are, further
explained in the next section.
2.2.3 New Assumption
Disasters increase an individual’s desire to seek group support in
place of a government of decreasing confidence.
3.2 Civilian Behavior
A natural disaster has the power to shape countries and change
societies [4]. A government can lose information of the area along
with the individuals within the affected area; during this blackout,
people may align with people or groups in which they feel satisfy
their needs and desires their government should fulfill. As these
groups gain strength in numbers, it soon becomes more difficult to
disperse and arrest all individuals via few police to enforce the
area.
Civilians can be categorized into four states: (1) Law-Abiding
Citizen, (2) Hawks, (3) Stealers, and (4) Jailed Citizens. The two
main states are the Law-Abiding and Hawks as these are the
classes that a civilian will be in the most. The behavior of a
civilian entering either one of these two states is based on a
transition equation, Equation 1. There are several factors that are
taken into account and compared against the individual civilian’s
personal threshold, a threshold set randomly between 0 and 1
across all agents. Should the factors of this transition function
exceed the civilian’s personal threshold, they would remain or
enter into Hawk mode, a state of actively steal resources should it
come into their view as they randomly roam the space; otherwise,
the civilian would remain or become a Law-Abiding Citizen,
moving in random fashion in a passive state while not pursuing
any illegal activities.
It is with Salgado’s assumptions and this new addition that we
hope to see how affiliation, group size, and the timing of
information-expanding policies would affect a society returning to
a state resembling pre-disaster conditions. However, this
implementation, just as the Salgado’s implementation, cannot be
proven to be a suitable model as information of post-disaster
zones is limited at best, restricted to eyewitness testimony and the
few recorded accounts of attacks and gangs that emerged from the
zone.
The remaining two states are an extension of the Hawk and LawAbiding classes, respectively. Stealers are active Hawks that have
86
stolen a single unit of resources and have begun their trip towards
their home of origin to hide their important item from the rest of
the world, diminishing the number of available units with an
adverse affect on the world; it is within this state that they are
their most vulnerable to other agents. In the event they are caught
by the police, they are rendered inactive, stripped of their stolen
item, are moved to their home and then placed on house arrest for
an arbitrary amount of time.
where P is an essential part of both the Expected Looting Utility
E(U) and Net Risk (N) for its role as the estimated arrest
probability, it would nullify any benefits that could have been
gained from being analyzing their compatriots within their view.
This is why Net Risk, as seen in Equation 5, is as it is, taking into
account the event if there is a zero arrest probability, establishing
the risk based on the fellow hawks within the civilian’s view (H)
in proportion to all the civilians in whichever mode in the same
area (TOT).
3.2.1 Algorithms behind Civilian Behavior
As previously stated, the civilian agent’s behavior is determined
by Equation 1, the transition function, dictated by what is seen in
the agent’s current field of view, the scarcity of agents and the
agent’s personal threshold of entering into a lawless state. As we
can see, there are two main values that are compared against the
agent’s threshold: the individual agent’s Expected Utility of
Looting (designated E(U)) and their Net Risk (designated N).
Just as the essential variables’ values are dependent on what the
agent sees, variables such as each agents’ view radius is
dependent on whether a disaster has occurred or not as a disaster
limits their field of receiving information. Equation 6 is the
formula that determines this. During non-disaster conditions (S =
0), each agent will have their maximum view to make their
decisions but as the system enters into disaster mode (S = 1), their
view is diminished by the magnitude of the disaster (MD) – the
stronger the disaster, the more affected the information an agent
will be receiving and processing will be. V and V* represents the
visibility radius of the civilians and law enforcement units
respectively.
Now, we enter the discussion of the civilian’s affiliation. Each
civilian will have two additional variables: a Tag and a Tolerance.
Initialized upon creation, each agent will received a uniformly
randomized Tag value between 0 and 1 while the Tolerance was
assigned to a normalized random Value with a mean of 0.5 and a
variance of 0.1672. This will symbolize the relative closeness
between an individual and a neighbor; this determination of
familiarity or strangeness is based on the tag difference between
the two against the threshold of the individual. An example would
be of such an individual with Tag 0.7 and Threshold of 0.6,
compared against a neighbor of Tag 0.3. By following Equation 7,
we can see that | 0.7 – 0.3 | = |0.4|. Being less than 0.6, the
individual would identify the neighbor as relatively close to them;
if the neighbor’s Tag was less than 0.1, then the individual would
felt relatively distance to the neighbor and not place them into
consideration.
The agent’s Expected Utility of Looting, as seen on Equation 2, is
based on the three distinct parameters: the Agent’s Private Benefit
of Looting (designated M), their Estimated Arrest Probability
(designated P), and their Private Cost of being Arrested
(designated C). While C is initialized to a constant, M and P are
dependent on external variables: M, as shown in Equation 3, is
based on the prior notion of M with the unlimited resources in a
non-disaster zone (S=0) and existing resources that are available,
or left, in the post-disaster world (S=1) in proportion to the
resource quantity that initially was available in the post-disaster
environment; this shows that an individual’s benefit of looting
increases as resources diminish. P, as seen in Equation 4, is an
extension of Epstein’s estimated arrest probability, modified to
take into account the proportion of the police (D) and hawks (H)
in the view. This is supposed to reflect how a person would
perform a daring action that has consequences when they have
confident associates providing backup and emotional support.
As each civilian finds others that are relatively close, they will
choose to move in random directions while attempting to keep a
majority of their neighbors within their view.
3.2.2 Law Enforcement
Compared to the civilian agents, Law Enforcement agents are
much more bare bones, acting as patrolling sentries moving in
random directions, sending any Stealers, Hawks that are currently
stealing items, to their home of origin and are placed under housearrest for an arbitrary amount of time once Stealers enter their
field of view.
We now look at the civilian’s Net Risk (N), the second half of the
transition puzzle. The Net Risk is to be evaluated based on the
civilian’s personal Risk Aversion (R), unique to each individual,
multiplied by the estimated Arrest Probability. However, there is
an inherent flaw in this design found when P = 0; in such a case
3.3 Post-Disaster Policies
Salgado’s paper expresses data containing Pre- and Post-Disaster
conditions for the team’s societies, see in Figure 1 above. It
demonstrates how in a society not experiencing a disaster, there
exists negligible Hawks, Stealers and Jailed citizens; this, of
course, is normal of any stable society as there will be individuals
who will have a low threshold, entering into thieving mode and
stealing when the opportunity arises. This changes when we are
shown a society when a disaster, or in this case an earthquake, and
society experiences as significant but rather low number of Hawks
and Stealers. As more people enter such a mode, there are several
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87
that succeed finding a window of opportunity to steal an item to
return to their home of origin; as this happens, the previously
infinite resources begins to drop dramatically, only furthering the
desperation of others, pushing more into Hawk status. With this
increase, more Hawks are able to view a larger area and begin to
accelerate their acts of thievery. This, however, reaches a point
where the amount of resources becomes ever scarcer, increasing
the number of Hawks in the system but few could ever find any
until all resources disappear and a grand majority of the
population have reached this desperate state. If this simulation
was allowed to continue, we would find that all stealers would be
rendered extinct and the remaining jailed civilians would be
released and most would join the Hawk Majority, unable to deal
anything.
times of desperation, continuously awaiting for relief effort
support as some still believe that the situation warrants more
extreme actions.
3.3.2 Implementation of Social Policy
The second policy deals with giving the affected population equal
treatment as the previous policy but only to the civilians. This
would be representative of local communication lines being open
to friends and family. While the previous policy demonstrated
such strength at any implementation time, this indeed does has its
flaws. Figure 3 shows early and late implementation of this and,
while the early implementation does indeed prevent chaos at such
a scale from allowing the limited resources from becoming
scarcer, this does not fall true for the late implementation. As
more people begin to steal more resources, the value of these
items rise; the introduction of this social policy does well in the
beginning but due to the larger view of the world combined with
the worth of these resources, it fails as civilians find these
windows of opportunities to return to Hawk mode and continue to
steal every now and then. This ultimately continues the stealing,
raising the resource value little by little until more and more
civilians enter Hawk mode, proving insufficient for long term
stability.
In such an isolated system, this would continue until the civilians
begin to die out from the lack of resources entering the system and
their inability to move on from the area in an attempt to seek out
more resources but this is reaching beyond the scope of the model.
Instead, this model would provide a rather grim view of what may
occur if support is not rendered within a suitable time frame. Thus
several strategies may be employed to prevent the decline of the
society. A point that will be made is that, while strategy is indeed
important, the timing of their introduction is just as important.
3.3.1 Reinforcement of Law Enforcement
3.3.3 Joint Policy
This policy is representative of returning communication and
strength to the police force to pre-disaster conditions. With this
expanded view of the world, Law Enforcement would be able to
cover more ground and arrest much more frequently, deterring the
loss of more resources to level out the desperateness of the
population. By looking at Figure 2, this graph [3] shows how
important of the introduction of such a policy can determine
whether a society will keep calm and carry on or enter temporary
Finally, we will be examining the idea of Joint Policy, the
implementation of both Law Enforcement Reinforcement and
increasing the Civilians’ field of view. With each of the individual
policies showing incredible strength at early insertion points, it
would be expected that the individual strengths would combine to
88
The remaining parameters are the civilians’ private variables. A
civilian’s Perceived Hardship and Risk Aversion (R) are
random values between 0 and 1 while their threshold (t) to
become a Hawk is a random value between 0 and 1.25. As for the
parameters that would be used to compared the individual to their
neighbors, each individual holds a Tag and Tolerance parameter
previously stated to be U(0,1) and N(0.5, 0.1672 ), as previously
stated. Lastly, Active? and Stealing? serve as Boolean flags that
signify if a citizen is a hawk and currently stealing resources,
respectively.
create a society that remains stable and very close to pre-disaster
continues, preventing the resource value drop to exceed a
breaking point and quelling any straggling stealers that may arise.
What is interesting is the late implementation: the breaking point
of the value of these resources is reached and wreaks havoc on the
society, initially quelling the society but only to have spikes with
little down time. While the police are able to crack down on any
Stealers, this does not stop opportunists to appear in pockets
around the society and steal when the chance arises; this leads to
continuous incarcerations of thieves as the situation is still
difficult. Regardless of the combined strengths of these two
policies, unless important and essential resources, such as food
and water, are quickly brought to the society, its people will still
continue to see this as a desperate situation, disregarding
outcomes for crucial needs.
4.2 Results
With our NetLogo program correctly replicating the original
results, the program could then be expanded to take the Tag and
Tolerance into consideration. While the results resemble
somewhat to the previous patterns, there are large and notable
differences that did emerge and caught the surprise of the
designers.
4. EXPERIMENTAL DESIGN & RESULTS
After establishing our model that we wish to implement, we can
now begin our experiment implementation. With the introduction
of familiar distance between each individual civilian that dictates
whether a civilian feels comfortable to perform Hawk-class
actions around those with similar Tags, even creating a group
based on these tags. We will use this addition of group dynamics
and cooperation to Salgado’s paper which viewed the disaster as a
purely individualistic model. With these changes, we will observe
the experiment results after the implementation of the information
policies and hope to see if the policies’ strengths are able to
produce the same effects as in the model prior.
4.1 Experiment Settings
To correctly examine the additions’ effects on the policies, we
first recorded the control scenarios for later comparison, one
establishing a disaster and one without. The first thing we can
observe is in the disaster free chart – seen on Figure 5(a); while
the plots do mimic normal low-level criminal activity, there still
exists a significant spike in arrested individuals. Since our
individuals will take other civilians of relative similarity into
account, they may go into sprees as a group, resulting in more
crimes and arrests. This can be thought of gangs in metropolitan
areas establishing their own “base” where similar individuals will
converge around; with the confidence of a larger group support,
the group may then perform more crimes but depending on the
police presence, it would be easier for law enforcement to arrest
and disperse the group. This would only be a temporary situation
as different groups would arise based on similar closeness from
the individuals’ tolerance.
The following experiment was programmed using NetLogo, using
the Rebellion model as a basis to modify and expand to our needs.
The area that will be used as the land of our society is established
to be 33 patches by 33 patches. In addition to the area parameters,
here are several pre-established values that were used are defined
on Table 1.
Table 1. Initial Parameter Values
Parameter
Value
Initial Cop
Density
0.74%
Initial
Resource
Density
Initial Agent
Density
Disaster
Magnitude
(MD)
Disaster Strike
Time
Early
Intervention
time
Late
Intervention
Time
k
5%
15%
8
50 Ticks
Parameter
Post-Disaster
Resource/Patc
h
Initial Private
Looting Benefit
(M)
Private Arrest
Cost (C)
Pre-Disaster
View Distance
(V)
Maximum Jail
Term
Value
30 units
0.2
0.2
In the Disaster-affected scenario – Figure 5(b), we can see that it
takes significantly less amount of time for resources to fall,
creating a hawk increase of a lesser strength as there are not
enough to go around; in each environment type, the number of
hawks does eventually plateau but it takes more time for the
numbers to reach to near-plateau levels. Once again, this may be
from individuals entering hawk mode to steal only when there are
sufficient group support to do so. The number of stealers, before
the number returns to lower levels, indeed show a more
widespread account, resulting to more exposure and more arrests;
these arrests, combined with the windows of opportunities for
gangs to commit crimes, would give much reason as to why it
may take longer. The emerging powers taking territory would
deter those more unrelated to them from stealing, slowing the
pace of resource depletion and would not send the society
spiraling towards a distressing situation as quickly.
10
10 Ticks
100 Ticks
Active?
false
350 Ticks
Stealing?
false
2.3
89
effect is shown on Figure 6(c) above. The Police’s range to
capture stealers is broadened but does not enough incentive for
them to stop their actions; while the force does indeed begin to
plateau the number of resources from being stolen, it creates a
police state type of situation as Law Enforcement send a
significant number of people to jail. The question then becomes
why does the Police Reinforcement at such a late time create more
stable control on resources compared to the early implementation?
It may be from the number of people that are being arrested. In the
early intervention setting, few are being arrested but the quantity
of resources continue to be chipped away by the stragglers and
when associates are released from jail around the same window,
the spikes in thievery would overwhelm officers for a time. In the
latter scenario, the number of hawks in the system is dramatically
higher, allowing more opportunities for the police force to
encounter Stealers moving the resources. From this, a larger
amount of people are incarcerated, preventing more hawks to join
in and preventing large gangs to be in a position to create more
widespread acts of larceny.
4.2.1 Reinforcement of Law Enforcement
The Reinforcement of Law Enforcement is one of the most
important aspects to returning a society to pre-disaster conditions;
as we’ve observed previously, the timing of their intervention is a
very important decision that may determine whether a society
would lose more resources and gain increasing lawlessness in the
land. As one would expect, they are able to do basically around
the same performance. The one key piece to observe is that, while
both systems do result in very similar initial results, after several
ticks, the differences begin to appear. Unlike the original system,
our system’s Hawks seem to continue on and enter thievery mode
in the over-confidence of group support while blinded by their
limited information of the area. This results in a high ratio of
Stealers being incarcerated to the number of actual Hawks in the
system. Based on the Hawk’s limited view, they do not find any
risk of stealing and blinding attempt to retrieve it; as such, many
are arrested. Sadly, this does not mean that there are not others
that believe the same way with the similar group support to
continue stealing. From the high number of incarcerations, the
police are preventing many from returning to their groups and
continuing such a mentality; this is why we begin to see the
number of incarcerations begin to lessen as time goes on, resulting
in more hawks to be taken into account. The police force may be
able to prevent many of the stolen goods from disappearing but as
time goes on, more hawks will incur more thievery as this can be
seen as the resources continue to drop in a faster rate over a longer
period of time.
4.2.2 Implementation of Social Policy
On the other side of the coin, the implementation of the Social
Policy – Figure 7- may not fully match the strength of a patrolling
force but does have its strengths, as previously discussed. It was
then surprising to see that, in contrast to the prior design’s success
in deterring this, Social Policy is only able to slow its pace, losing
significant ground during Hawk spikes, as seen on Figure 7. With
the disaster occurring after 50 ticks and Police Reinforcement
entering relatively quickly after, occurring at 100 ticks – Figure
7(a), the additional support seems to be insufficient. In this
experiment with the established parameters, only 8 police agents
exist to roam the world and arrest Stealers, once again, Stealers
are Hawks who are actively carrying a stolen resource, within
their expanded field of view. This support is unable to arrest many
of the thieves, draining resources and creating more of a desperate
situation for the rest of the society. What are important to observe
are the moments where Hawks and Stealers spike; these spikes are
not instant and significant but are smaller and consistent. The
arrested Stealers being replaced by more Stealers extended the
stealing spree’s longevity, seeming to be the likely culprit,
exploiting the limited police force’s ability of arresting more than
one at a time.
Once again, our late implementation begins when resources are
depleted. We then change the intervention point to 225 ticks into
the simulation – Figure 7(c) below. Interestingly, the intervention
does follow a very similar route as the original system design.
Upon introduction, it slows down the Stealers’ rate of thievery but
only initially, as they spike as the number of Hawks spike,
ultimately losing ground after a short period of time. What is
interesting about the result is how the result came about. Many of
As for the late intervention, a similar situation occurs here
compared to the previous system’s scenario; however, by the late
timing of the policy introduction, resources were depleted. The
program was tweaked to observe at an earlier time. A different
90
the same situations occur between the two but the rate in which
resources are depleted is different. Rather than creating a
significantly slowing plateau of dropping resources, what we see
are more attuned to minor speed bumps: there is some slow down
in which the resources are being stolen but it doesn’t stop the
inevitable, resulting in depleted resources a short time after what
Figure 5(b) demonstrates to be average depletion time. Because of
the civilians’ expanded view of the world, they are able to see
more police and add it into their risk equation. At the same time
however, they are able to see more civilians, i.e. more
compatriots. While police agents are indeed deterrents to
lawlessness, the number that exists in the world isn’t enough to
stop many stealers from appearing in minor but lengthy spikes,
increasing the worth of the remaining resources, repeating the
same pattern until all are depleted.
confidence in those they consider their fellow compatriots,
creating an environment that strengthens an individual’s resolve to
find resources. This may be why, as supported by the previous
figures, there still continues to be people to steal, forcing Law
Enforcement to continuously arrest, only slowing down the rate of
resources stolen, lacking the numbers to act as a punishable
deterrent to civilians. While the policy does indeed create an
environment that resembles a pre-disaster society, unless relief
efforts to bring additional resources and help repair the
infrastructure soon, the society will only stay at such levels for
only so long.
Once again, the late intervention proved too late to influence the
situation – figure 7(b) so the simulation ran with intervention
occurring at 250 ticks – figure 7(c). Unlike the early intervention
which created a more stable environment, the number of resources
and their worth were at such a point that intervention, while trying
to stabilize the society, creates a more overwhelming scenario.
This is comparable to Figure 6(c), the Police Reinforcement’s late
intervention, where a higher amount of Stealers and Incarcerated
Civilians arise. While enforcing with a lower number of jailed
individuals, Stealers were more pervasive in the world, reaching
to a constant and relatively high level which lead to more jailed
civilians but, most importantly, still stealing resources at a rate
until resources eventually disappear. As the resources reaching
dangerously low levels, there are not enough for Hawks to steal,
increasing their Hawk population while the Police Force are find
it harder to find Hawks that were actively stealing.
4.2.3 Joint Policy
5. CONCLUSION
Last is the Joint Policy, one expected to continue to have the
strength and influence to prevent or significantly stall the descent
of the society into chaos. For the most part, the policy does just
that, as seen on Figure 7, but not to the effect that many wish it
had. As we observe the early intervention of this joint policy
between Law Enforcement Reinforcement and a Social Policy on
Figure 7(a), it is able to bring down the number of Hawks and
Stealers sharply, preventing the numbers from entering higher
levels. Afterwards, however, the society still has several
problems. Due to this being a disaster where the previously
unlimited resources are now limited, the value of resources still
remain high while there may be many resources still available;
this does not prevent groups of people to take advantage of the
situation. In a non-disaster zone, people still steal based on their
view of opportunities but that is only a small minority; in a society
affected by disaster, this only increases that number as the
resource value is raised higher and civilians are finding
The addition of mob mentality, civilians forgoing their private
cost of being arrested by their group support of similar civilians –
whether it is race, creed, or like-mindedness, is an important
aspect to consider during the reconstruction of a devastated area.
With the loss of essential resources and a strong authority, groups
of people may arise to take advantage of the power vacuum that
occurs as information blinds both the affected and those that wish
to provide many forms of relief. Epstein’s work on modeling
social violence between people based on another’s aspects was
instrumental to create a more fleshed out idea and image that
Salgado’s team’s work want to convey and demonstrate. The idea
of increasing the information received by the police force and the
civilian population was expanded to several polices that, initially,
looked sufficient to teach important lessons of what must be
returned to the affected area and when. Their method, however,
only looked upon the individuals while not taking into
91
consideration other forces that may arise. While all three policies
– Police, Social and Joint – are still important and very influential
policies, the strongest policy, being the Joint Policy, is not the
silver bullet that the previous paper made out to be when it went
against the emerging groups and behavior that occurred in our
system. While it is a given, based on the data, that an earlier
intervention does indeed have a more significant and beneficial
result for returning to the society to pre-disaster conditions,
simply having the strategy is not enough to combat the groups
acting as multi-organisms made up of individual and unique
organisms.
These gangs, organizations and mini-societies prove to be another
individual for the policies to attack against. The main basis of
combating them already exist, as we’ve shown, but needs to be
organized in a better way. One possible extension to this would be
consideration of the coordination and positional organization of
the police force, breaking down the society area to more
manageable sections that would not overwhelm the few and
randomly roaming police force. The problem with these ideas and
findings is that this is based on assumptions and the limited
information gathered from ultimately inadequate and inaccurate
sources; if one were to try to attempt these strategies, the best way
to do so would be to gather information as a society reels from a
recent devastating event to gain better insight as to what is
required for these models to become more accurate
representations. However, due to the strengths and established
influence of the papers and strategies this paper is based on, our
experiment does create a stronger theoretical view on the idea.
6. REFERENCES
[1] Epstein, Joshua M., and Robert L. Axtell. Growing artificial
societies: social science from the bottom up. MIT press,
1996.
[2] Epstein, Joshua M. "Modeling civil violence: An agent-based
computational approach." Proceedings of the National
Academy of Sciences of the United States of America
99.Suppl 3 (2002): 7243-7250.
[3] Bhavnani, Rakhi. "Natural disaster conflicts." Unpublished
manuscript, Harvard University (2006).
[4] Kim, Jae-Woo and Hanneman, Robert (2011) 'A
Computational Model of Worker Protest' Journal of Artificial
Societies and Social Simulation 14 (3) 1
<http://jasss.soc.surrey.ac.uk/14/3/1.html>.
[5] Salgado, Mauricio, Elio Marchione, and Alastair Gill. "The
calm after the storm? Looting in the context of disasters."
(2010).
92
Multi-agent based modeling of Selflessness surviving
sense
Taranjeet Singh Bhatia and Ivan Garibay
Dept. of EECS
University of Central Florida
4000 Central Florida Blvd, Orlando FL 32816
{tsbhatia, igaribay}@cs.ucf.edu
ABSTRACT
in order to describe this nature. Many of such biological behaviors are explained as kin-related. However, altruism goes
beyond any kinship or reciprocity where people are willing to
support unrelated and unknown people even when it requires
cost and no intention of earning returns [8] [6] [2]. Examples
include institutional learning, parenting, knowledge transfer, warning notification, or helping hands in the holocaust.
Moreover, all the published literature and research on altruism concentrated on relatedness and reciprocity. Therefore,
our work tries to present the true nature of altruism in the
form of selflessness and avoiding amalgam of kinship and
reciprocity with altruism. In this paper, we experimented
over the simple model of unconditional altruism labeled as
selflessness and emergent properties related to the size of
the population. The evolution of altruism is a paradox of
fitness theory, which states that an organism can improve
its overall genetic success by cooperative social behavior. A
person carrying the altruistic gene trait can only spread it to
the rest of the population if the mean fitness of the person is
higher than the population average fitness. Therefore, if one
defines altruism at the fitness level of the population, then
it can never evolve because an altruistic carrier enhances
the fitness of others more than its own. Social model of
human nature is highly dependent on environmental issues,
which arise due to the collective action of many independent agents such as pollution, humor spread or an act of
revolution. Therefore, we require a multi-agent platform, to
model the understanding of the emergent nature of collective actions. In this paper, the sole purpose of the agent
is to gather food for the purpose of survival, in the simulation environment where distribution of food variation occurs
dynamically. Section 2 compares the work with earlier research on altruism. In Section 3, we discuss the motivation
and background history related to the concept of selflessness
in society. In Section 4, we explain the simulation setup and
rules involved in the environment. Section 5 depicts and
explain the outcome of the experiments.
Almost all of the literature defines an Altruist as a person
who increase price or weight of others. The definition emphasizes more on the price of altruism, but it fails to mention the motive of an agent or group displaying the nature
of self-sacrifice. In this paper, selflessness replaces the altruism which is likely to be stronger towards the Kith and
kin because of - organismic causation, reciprocative benefit
and better chances of gene transfer to the next generation.
Moral values seem to be implicated in altruism such that
personal norms are self based standards for specific behavior and decision making such as charity. On the other hand,
sometimes people feel some degree of moral obligation, not
to give help to some individual or group. We experimented
on the attribution of Sugarscape with selflessness and charity norms, in order to justify that a society with negative
personal norms grows less than a people having no norms of
helping others selflessly.
Categories and Subject Descriptors
I.2.11 [Complex Adaptive Systems]: Artificial Intelligence—Multiagent systems
General Terms
Human Factors, Economics, Experimentation
Keywords
agents, social models, simulation, sugarscape
1.
INTRODUCTION
Cooperation and Collaboration have been widely studied
in various disciplines, such as biology, socio-biology, behavioral science, and engineering. The unidentified nature of
ground squirrel giving an alarm call to warn its local group
about the presence of a predator by putting itself in more
danger remains in a state of debate even after centuries of
learning and investigation. Karl Pearson [9], Charles Darwin [5] and Hamilton [7] introduced various terminologies
as individual favors, group favoritism and kin-relationship
2.
RELATED WORKS
Altruism is a part of human nature and being heavily reviewed in social psychology, and to a lesser degree in sociology, economic, political behavior and sociobiology. Darwin’s
natural selection rule definitely works in cooperation between relatives. When parents provide food to children, this
increases the fitness value of the child for survival as does the
chance of parent for successfully passing through its genes.
When strangers come together to help, one person gets the
benefits and other willingly incurs loss, but there would be a
0
93
gain in the long term. Trivers [12] defines this co-operation
between non-relative individuals by means of reciprocal altruism. Wilkinson [14], who studies the behavior of vampire
bats, used simulations to calculate the benefit of these altruistic acts. Wouter Bulten [3] extended the same concept
with the sharing blood phenomena of vampire bats. Bulten’s
simulation focuses on cheater agents who do not reciprocate
the altruistic act. Bench-Capon [1] introduces the altruism
in the decision making process of the agents to model empirical behavior by people playing the Ultimate game in experimental situations. Jung-Kyoo Choi [4] demonstrated the coevolution of parochial altruism in a war like situation, where
altruists bear the cost of giving aid to both the insiders and
outsiders, and punish those who violate norms. However,
the Parochial altruists would give preferential treatment to
their own members and punish those who harm the group
more severely, than if the victim is not an insider. All the
aforesaid altruism studies were based on the kinship or reciprocal altruism, where agents have intentions of gaining
substantially in the long terms. There are several examples
which go beyond the kinship and reciprocity, and people are
willing to support strangers, where they don’t take any assumption of receiving back the same in the course of time.
Nemeth and Takacs [11] implemented Teaching as an example act of true altruism, wherein the knowledge transfer
enhances the survival chances of the recipient, but reduces
the reproductive efficiency of the provider. All the simulations in this paper were performed using the multi agent
based system, considering the act of giving as attribute of an
altruistic agent increases the fitness of all the other agent in
the vision proximity. In the real situations, humans’ act of
altruism contains the element of rational thinking in order
to decide the percentage of donation or charity or help to
others. This thinking can be performed irrationally over all
the agents in equal proportion and simultaneously.
3.
and sharing and consuming together, are three pillars of
Sikhism faithfully followed by members of this community.
This religion has demonstrated many examples of selflessness for the welfare of another religion, country or person
which many time concluded with self sacrifice. Sikhs have
a religious obligation of performing the act of donating ten
percent of one’s harvest, both financially and in the form of
time and service to society which makes this religion true
in displaying selflessness. Though being under long holocaust period, this religion managed to flourish around the
world as fifth largest religion in a short span of 400 years.
This religious sect provides us the motivation for simulating
the multi-agent based social modeling of selflessness over the
extremely simple rules of society.
4.
EXPERIMENTAL STUDY
All the simulations were performed on the Sugarscape
Model [10]. This work extended the NetLogo model of Sugarscape model [13]. Agents are endowed with sugar, vision,
metabolism, charity and selflessness values. In the initial
setup, agents are initialized with a random value of wealth
(sugar) between 5-25, vision range between 1-6 in order to
search and increase wealth, metabolism of 1-4 for spending
wealth in each time tick, and max age factor between 60-100
time ticks. The amount of sugars each agent collects is considered as his or her wealth. Charity attribute defines the
religious obligation of the individual which he has to obey
in life. Charity value is invested by an individual at all cost,
either facilitate to needy or by making a donation to social
organization. Agents perform the charity even though it
does not contain any selflessness factor or altruistic factor.
Many societies believe in giving charity equally distributed
to all the receivers without exceeding the charitable percentage. This percentage attributes vary between 0-10% of
every new income gain. Selflessness attributes defines the
true altruistic behavior possessed by individuals. Selflessness acts under the following cases such as saving the life
of unknown, sacrifice made by one soldier for saving many
others or simple act of sharing food. Unlike charity, Selflessness is not mandatory to perform but happens under the
circumstances. Agents carry the Selflessness in the range
of 0-100%, where, 0 simply means extremely unrefined behavior and 100 signifies the self sacrificing nature. Unlike
other altruistic simulations, we are considering the rational
judgment of humans while performing charity in the environment. Humans give charity to the needy person and avoid
spending wealth randomly for everyone. All the agents in
the simulation are governed by the following rules:
MOTIVATION
The concept of altruism has been heavily studied and debated. Research on the collective actions of insects and animal behaviors show that the altruism in human society is
fairly misconceived as kin-related. Selfless actions of human
beings were untouched presumingly the view that selfishness
are required for increasing the fitness index of the population. Dictionary meaning of Selflessness is ŞThe quality of
unselfish concern for the welfare of othersŤ. This word is
very often associated with religious code of conduct. Major religious orders such as Christianity, Islam, Buddhism,
and Sikhism prescribe and preach the concept of Selflessness.
Interest in investigating the emergence attribute of Selflessness originates from the fast growing, often misunderstood
religion formally known as Sikhism. The brief history of
this sect of society is necessary in order to understand its
claimed existence as the fifth largest and the youngest religion in the world. Sikhism is a monotheistic religion founded
during the 15th century in the Punjab state of India by a
person known as Guru Nanak Dev. During the 16th century, India was invaded by the Mughal rulers of Afghanistan
who entered through Punjab, which caused significant loss
of Sikh population. Later, under the British rule, partition
of India divided Punjab into two parts. The state of Punjab has been under long suppression from Mughal Invaders,
British empire, partition riots, terrorism from Pakistan and
political massacre. Daily practice of meditation, Honesty,
• Agents collect the sugar in order to survive or increase
the wealth
• Every time ticks, agents consume sugar as per the
metabolism
• Agents have vision range to look for the food in all
possible directions
• Agents in their vision range look for the other agents
having lower wealth than oneself
• Charity percentage equally distributed to all neighboring agents who have 10% wealth left
94
Figure 1: Sugarscape experiment without selflessness with constant sugar growback
Figure 2: Sugarscape experiment with selflessness
under constant sugar growback
• Selfless percentage applied to randomly selected agent
with no sugar or less than 1
Rules for the patches are similar to the Sugarscape model.
Sugar grows back on the patches in three ways: Constant
grow back, Random grow back, and No grow back. We
can switch between any of these features during simulation. These features enable us to present the effect of famine
on agent population. Normal famine demonstrated by random grow backs of sugar on the landscape, whereas a severe
famine applied using No grow back of sugar on the landscape
for a certain length of time ticks.
5.
RESULTS
Three cases were considered for the simulation where improvement in the agent population count, Gini-Index, Variance in vision and Variance in the metabolism of the resulting agents have been evaluated. The Gini coefficient measures the inequality among the values of a frequency distribution. A Gini coefficient of zero expresses perfect equality
where all values are the same, for example, where everyone has an exactly equal income. A Gini coefficient of one
(100 on the percentile scale) expresses maximal inequality
among values, for example, where only one person has all
the income. All instances of the experiment were performed
on a population size of 500 and time length of 200 ticks.
All the data statics were generated with a confidence level
of 95% and 10 iteration of each case. ‘a’ on x-axis in the
graph demonstrate the result with no selflessness and charity where as ‘b’ on x-axis shows the simulation result with
the selflessness and charity factors.
In the first experiment, we provided the Sugarscape landscape with constant sugar grow back as shown in Fig 1. In
Fig 5, Population count has increased by the 37% where
value jumps from 310 to 424 in population size. In Fig 6,
Figure 3: Sugarscape experiment with selflessness
under random sugar growback
Gini-index of the agent wealth increases by 24%, In Fig 7, no
significant variation has occurred in the vision distribution
of agents. In Fig 8, large increase of 96% has occurred in
metabolism variance of the agent population survived after
200 time ticks. Initially, without any charity or selflessness
factors, all the agents have a sole purpose of acquiring the
sugar peak for greater wealth collection. The agents with
a broader vision and lower metabolism have a high proba-
95
Experiment 1
Experiment 2
Experiment 3
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
a
b
Figure 6: Gini-Index for experiment 1, 2, and 3. (a)
without selflessness (b) with selflessness
Figure 4: Sugarscape experiment with selflessness
under famine circumstance of no sugar growback
Experiment 1
Experiment 2
Experiment 3
3.2
Experiment 1
Experiment 2
Experiment 3
3.1
500
450
400
350
300
250
200
150
100
50
0
3
2.9
2.8
2.7
2.6
2.5
2.4
a
a
b
Figure 7: Vision Variance for experiment 1, 2, and
3. (a) without selflessness (b) with selflessness
b
Figure 5: Agent population size for experiment 1, 2,
and 3. (a) without selflessness (b) with selflessness
who never came in the contact of any agents with sufficient large selflessness factor die before reaching the peaks
of Sugar Mountains. A 96% increase in the metabolism variance shows that later simulation contains more unfortunate
agents than previous simulation.
In the second experiment, Sugarscape landscape has random sugar grow back on every patch as shown in Fig 3. In
this experiment, all agents are uncertain about the sugar
they will collect in the next iteration which makes no significant difference in the population count with or without selflessness as shown in Fig 5 case ‘b’. Vision range distribution
in the population has increased by 2% as well as Metabolism
range distribution in the population has increased by 77% as
shown in Fig 7 and Fig 8 respectively. Due to the randomness in the sugar growth, most unfortunate agents die very
bility to reach the peak and stay there for the rest of the
time. The agents with narrow vision and higher metabolism
suffer from starvation during the travel, due to slow speed
and not enough sugar collection for satisfying metabolism
they die early. In the second simulation as shown in Fig 2,
where agents are allowed to perform charity and show off
selflessness have shown significant improvement on the population size survived after the stipulated 200 time ticks. In
this simulation, all the fortunate agents with a broader vision and lower metabolism help the unfortunate agents with
narrow vision and higher metabolism to reach the peak while
they traverse toward the peak. Only the most unfortunate
96
Experiment 1
Experiment 2
including more complicated model of society including family planning, culture dispersion, income rate, geographical
advantage, and the concept of spiritual strength associated
with the religion.
Experiment 3
1.4
1.2
7.
1
[1] T. Bench-Capon, K. Atkinson, and P. McBurney.
Altruism and agents: an argumentation based
approach to designing agent decision mechanisms. In
Proceedings of The 8th International Conference on
Autonomous Agents and Multiagent Systems-Volume
2, pages 1073–1080. International Foundation for
Autonomous Agents and Multiagent Systems, 2009.
[2] S. Bowles and H. Gintis. Origins of human
cooperation. Genetic and cultural evolution of
cooperation, pages 429–43, 2003.
[3] W. Bulten, W. Haselager, and I. Sprinkhuizen-Kuyper.
Sharing blood: A decentralized trust and sharing
ecosystem based on the vampire bat.
[4] J. Choi and S. Bowles. The coevolution of parochial
altruism and war. science, 318(5850):636–640, 2007.
[5] C. Darwin. The descent of man (amherst, ny, 1998.
[6] H. Gintis. Strong reciprocity and human sociality.
Journal of Theoretical Biology, 206(2):169–179, 2000.
[7] W. Hamilton. Innate social aptitudes of man: an
approach from evolutionary genetics. Biosocial
anthropology, 133:155, 1975.
[8] J. Henrich. Cultural group selection, coevolutionary
processes and large-scale cooperation. Journal of
Economic Behavior & Organization, 53(1):3–35, 2004.
[9] P. K. Fortnightly review. 56, 1894.
[10] J. Li and U. Wilensky. Netlogo sugarscape 1
immediate growback model@ONLINE.
[11] A. Németh and K. Takács. The evolution of altruism
in spatially structured populations. Journal of
Artificial Societies and Social Simulation, 10(3):4,
2007.
[12] R. Trivers. The evolution of reciprocal altruism.
Quarterly review of biology, pages 35–57, 1971.
[13] U. Wilensky. Netlogo@ONLINE.
[14] G. Wilkinson. Reciprocal altruism in bats and other
mammals. Ethology and Sociobiology, 9(2):85–100,
1988.
0.8
0.6
0.4
0.2
0
a
b
Figure 8: Metabolism Variance for experiment 1, 2,
and 3. (a) without selflessness (b) with selflessness
fast because fortunate agents donŠt have enough wealth to
distribute to others.
In the third experiment, we tried to model the famine
effect on the Sugarscape landscape by turning off the sugar
production for 50 time ticks after the constant grow back of
150 time ticks, as shown in Fig 4. In the case of selflessness
and charity, 27% more agents survived as compared to no
selflessness as shown in Fig 5. An increase of 147% in the
Gini-index shows the great jump from 0.27 to 0.68 as shown
in Fig 6. This means that in the case ‘a’ of no selflessness,
only the rich and wealthy agents in total sugar after 150 time
ticks, manage to survive the famine of 50 time ticks, whereas
unfortunate and poor agents wipe out very fast. In case ‘b’,
Gini-index moved to 0.68 levels of inequality of wealth in the
population which signifies that almost all types of agents are
surviving in case of selflessness. Again metabolism variance
has increased from 0.25 to 1.20, which signifies that wealthy
and fortunate agents are constantly feeding the other less
fortunate agents during the famine period of 50 time ticks
as shown in Fig 8. In case where we increase this famine
period to 100 time ticks, the whole population will die out
simultaneously in case of selflessness, whereas, in the earlier
case it will die out one by one and slowly.
This experiment has shown the interesting emergence of
metabolism variance of agents in the population due to the
addition of the famine in the simulation.
6.
REFERENCES
CONCLUSION
In this paper, we perform the multi agent based simulation of Sugarscape model with the addition of charity and
Selflessness in agents’ attribute. The results of the experiment demonstrate the significance of these attributes when
associated with agents helping more agents to survive, in
the normal as well as in the famine condition of Sugarscape
landscape, even when no sugar is available for an agent to
collect or consume. These experiments contributed beneficial findings to the long lasting discussion over effects of
pure altruism in the society. Above experiments are very
basic finding in this direction, we want to elaborate the work
97
College of Engineering and Computer Science, University of Central Florida, 4000
Central Florida Blvd. Orlando, Florida, 32816
The Effect of the
Movement of Information
on Civil Disobedience
Yazen Ghannam
November 27, 2012
Agent-based computational models are a useful tool in modeling
complex adaptive systems. Due to the wide availability of computing
resources, these models are increasingly being used by researchers to
generate complex phenomena. Even with the availability of modern
computing resources, researchers still approach complex systems by
modeling a single abstract layer in the system’s hierarchy. It seems to
be common practice to take a simple model and extended to include
more complex phenomena while remaining in a single layer in the
hierarchy. In this paper, I propose taking a simplified model of civil
disobedience within a nation and extending it to include a simplified
model of the movement of information between nations.
98
easily distributed between nations. It is now
common for an individual to maintain
relationships with other individuals through
various mediums including cell phones
(voice calls and text messages), email,
internet social networking sites, etc. These
mediums are fairly low cost and easily
accessible even in developing nations.
Furthermore, information can be
disseminated very quickly through many
popular social networking websites.
1 Introduction
T
his paper presents some extensions to
the agent-based computational model
presented by Epstein [1]. In Epstein’s model
of civil disobedience there are two types of
agents, civilian agents and cops. Civilian
agents have the ability to participate in
active rebellion based a set of rules and
parameters. In short, a civilian will rebel if
its grievances outweigh its sense of net risk.
Part of a civilian’s grievance is its perceived
Legitimacy of its government. In Epstein’s
model, this Legitimacy is completely
exogenous and is controlled by the
researcher.
2.2 Related Populations
Even though information is easily
accessible, it may not have a strong impact
on the general population of a nation. This
may be true for various reasons, one of
which may be that people are only
interested or affected by information
regarding others of similar characteristics.
These characteristics can be geography,
language, economic system, etc. For
example, it may be that the general
population of the United States “feels”
more closely related to the population of
Japan than to the population of Hungary,
and so news from Japan may have more
weight than news from Hungary.
One of the extensions I present in this
paper is the notion that the perceived
Legitimacy of a government is affected by
the perceived Legitimacy of other
governments. This interrelated effect is
further enhanced by the speed at which
information travels in our modern era.
These two phenomena are part of a larger
phenomenon of Globalization.
The purpose of the work presented in this
paper is to create a simplified model of the
effect of Globalization (macro-model) on
individual populations of agents (micromodel).
An actual example in recent times is the
wedding of Prince William being more of an
interest to the U.S. general population than
many of the uprisings and revolutions
happening throughout the Arab world.
Another example is how even within the
Arab world many revolutions happened in
similar nations (those with dictatorships)
and general protests in others (those with
monarchies).
2 Background
2.1 Global Telecommunication
Modern telecommunication systems have
facilitated the creation of global social
networks and allowed information to be
99
This idea of “related populations” is very
complex, and it would be very difficult to
develop a quantitative index of how every
nation relates to every other nation.
Nevertheless, even without knowing the
exact relations between real nations, I feel
that a general model can be developed to
represent this behavior.
The Legitimacy of a nation depends on the
Legitimacy of all the nations and their
relative “distance” in terms of
characteristics from the current nation. This
rule takes into account the effect of the
current nation on itself. Every time step, a
new Legitimacy is calculated for all the
nations from the old Legitimacy values.
3 Implementation
3.2 Simplified Effect of the State of a
Nation on its own Legitimacy
3.1 Movement of Information
between nations
Our current model of civil disobedience
assumes that the perceived Legitimacy of a
government is completely exogenous to the
nation. This doesn’t seem to be a very
realistic assumption as the state of affairs
within a nation can also have an effect on
the Legitimacy of a government. Others
have attempted to model this behavior in
more detail. One such example is “MASON
RebeLand” [2] in which the authors’ model
of a nation includes natural resources,
polity, etc.
This extension involves the simultaneous
modeling of multiple nations and their
effect on one another. In addition to the
rules and parameters from Epstein’s model,
I propose two new parameters and one
new rule. The first new parameter is the set
of nations (N). Each nation in N is an
instance of Epstein’s (base) nation model. In
addition to all the parameters it inherit
from the base model, each nation will have
a new parameter (c) representing its “set of
characteristics” drawn from U(1, |N|).
Values of c that are closer together
symbolize that the nations they represent
are more closely related. From these two
new parameters I derive a new rule for
finding the Legitimacy (L) of a nation.
∑|
∑|
|
‖
|
‖
In order to maintain simplicity for this
paper, I chose to abstract away the details
of intra-national events. I propose that the
perceived Legitimacy of a government is
affected by the number of active agents in
the nation. The more active agents present,
the lower the perceived Legitimacy. This
effect is weighted and added to the
international effect. This creates an internal
pressure that can pull up or push down the
perceived Legitimacy.
‖
‖
100
4 Experiments
throughout the continent recognized the
similarity between their governments.
For all my experiments, I used NetLogo [3]
and extended the “Rebellion” model [4]
from the NetLogo library. Five nations were
instantiated. The Legitimacy update rule
was modified to include a scaling factor, s,
for the distance between c values (s*|c-ci|).
This was done to allow the observation of
more distributed behavior due to the
limited number of nations.
4.1.2 Effect of Decreased Legitimacy in
Single Nation on Neighboring Nations
Ni-1  Ni  Ni+1
The effect of the Legitimacy decrease
spreads outward from the single nation to
those nearest to it. The drop in Legitimacy
of neighbors is relatively small. Eventually,
the Legitimacies of all nations converge to a
similar value (Fig. 2).
4.1 Extension 1
4.1.1 Effect of randomly initialized
Legitimacy for all nations
The Legitimacy of each nation was
initialized to a random value between 0 and
1. After a finite number of steps, the
Legitimacies of all nations converge to a
similar value (Fig. 1).
This behavior models the effect of the drop
of Legitimacy in a single nation due to some
external event. An example of this behavior
could be the American Revolution. As the
Legitimacy of the British monarchy fell in
the eyes of the American Colonists, other
nations in similar circumstances, such as
France and Mexico, would show a drop in
perceived Legitimacy of their respective
governments.
This behavior models how, in the absence
of any external factors, the perceived
Legitimacy of a nation approaches a similar
value to that of other nations related to it.
This phenomenon may be rarely observed
in history due to the effect of external
factors such as weather patterns,
technological advances, etc.
A more recent example would be the Arab
Spring. As the Legitimacy of the Tunisian
government fell, similar governments in
Libya, Egypt, Yemen, and Syria went
through similar changes. Even though these
nations are not connected geographical and
are not necessarily culturally similar, they
had enough similarity in other
characteristics to result in similar events.
One possible example may be Medieval
Europe. Different governments would have
had different initial Legitimacies. Some
would have been native-born kings, while
others would have been foreign invaders.
Eventually, the nations would influence
each other through different methods of
communication. Then the perceived
Legitimacies of all the governments would
converge to similar levels as the people
4.1.3 Effect of Decreased Legitimacy in
Two Nations on Middle Nations(s)
Ni-1  Ni  Ni+1
101
The effect of the Legitimacy decrease
spreads from the two nations to the
outward nations and the middle nation. The
effect on the outward nations is relatively
small compared to the effect on the middle
nation. Eventually, the Legitimacies of all
nations converge to a similar value (Fig. 3).
higher perception of the government’s
Legitimacy.
These experiments were run again while
allowing agents to remain active even when
in jail. This caused the Legitimacy to
eventually reach zero without increasing
again.
This behavior is similar to the behavior of
the single nation. The key difference is the
compounding effect on the middle nation.
4.3 Convergence
For every experiment, the Legitimacies for
all the nations would converge to a similar
value (Fig. 4). For every run, the simulation
was stopped when the difference between
the current Legitimacy of a nation and its
Legitimacy from the last step was less than
a threshold of 0.001 for all nations.
4.2 Extension 2
All the above experiments were rerun with
the Local Weight set to 1.0. The results
were similar in that the Legitimacies of all
nations eventually converged to similar
values. Before they converged, the Local
Weight and the ratio of active agents would
pull the nation’s Legitimacy down. This
would cause more agents to become active,
and so on. As more agents become
deactivated (jailed), the Legitimacy slowly
increases. The nation reaches an
equilibrium point based on the length of the
maximum jail-term. With longer jail-terms,
the Legitimacy will eventually increase to a
value close to 1.0. With shorter jail-terms,
the Legitimacy will remain at lower value.
Each of the different experiments had a
different range in the number of steps
required to converge. The simulations with
random initial values within 10 to 17 time
steps. The simulations with a single low
initial Legitimacy would converge
differently based on which nation was the
“low” nation. The nations towards the
“middle” of the spectrum would allow the
set to converge more quickly, since they
affect and are affected by more nations that
those that are towards the “edges”. The
simulations with two initial low Legitimacies
largely had about the same rate of
convergence. This is most likely due to the
limited resources in this particular
implementation, since two nations from a
set of five is a large fraction.
This behavior is similar to what may happen
after government suppression of uprisings.
As the Legitimacy of a government falls,
more civilians view the government as
illegitimate and Legitimacy continues to fall.
But if the government is able to suppress
the uprising and any knowledge of it, then
newer civilians enter the nation with a
102
5 Future Work
I believe that the study of complex adaptive
systems using agent-based computational
models should move past the modeling of
single closed systems and begin to model
multiple hierarchies of systems. In this
regard, I hope that the extensions
presented in this paper can be seen as a
good first attempt at multi-layered systems
modeling.
There are many more possible extensions
that are worth exploring. Many of these are
based on the idea of having heterogeneous
nations. Currently, all nations in the set
have the same jail-terms and local weights.
It is clear that jail-terms have an effect in
regards to the internal perception of a
government’s Legitimacy. It would be
interesting to have each individual nation
use a unique maximum jail-term sentence.
In addition, varying the local weights
between nations would be more realistic.
Not all nations treat information of others
with the same weight. Some are more
isolationist than others.
Works Cited
[1] J. M. Epstein, "Modeling civil violence: An agentbased computational approach," in Proceedings
of the National Academy of Sciences of the United
States of America, vol. 99, May 14, p. 7243-7250,
2002.
Another possible extension that I feel would
be valuable is the modeling of the migration
of peoples. This would be especially
interesting with respect to migration due to
the perceived Legitimacy of governments.
Issues relating to foreign militants and
refugees from one nation can have an
effect on issues within neighboring or
similar nations.
[2] C. Cioffi-Revilla and M. Rouleau, "MASON
RebeLand: An Agent-Based Model of Politics,
Environment, and Insurgency," in Proceedings of
the Human Behavior-Computational Modeling
and Interoperability Conference, Oak Ridge, 2009.
[3] U. Wilensky, NetLogo.
http://ccl.northwestern.edu/netlogo/, Evanston,
IL.: Center for Connected Learning and ComputerBased Modeling, Northwestern University, 1999.
6 Conclusion
[4] U. Wilensky, NetLogo Rebellion model.
http://ccl.northwestern.edu/netlogo/models/Reb
ellion, Evanston, IL.: Center for Connected
Learning and Computer-Based Modeling,
Northwestern University, 2004.
In the absence of external events, the
perceptions of governments by their
peoples eventually reach a sort of
equilibrium. I feel that this is a valid
representation of various social behaviors. I
present this work as a baseline for future
works. I hope that experts in various fields
will validate, correct, and extend this model
as they see fit.
103
Figures
Figure 1: Random Initial Values
Figure 2: One Low Legitimacy
104
25
Frequency
20
15
10
5
0
10
11
12
13
14
15
Steps to Converge
Figure 3: Two Low Legitimacies
Figure 4: Frequency of Steps to Converge
105
16
17
The Effects of Hygiene Compliance and Patient
Network Allocation on Transmission of Hospital
Acquired Infections
Zachary Chenaille
University of Central Florida
Department of Electrical Engineering and Computer Science
Orlando FL, USA
zchenaille@knights.ucf.edu
Abstract—Hospital acquired infections account for large
amounts of deaths and increased costs in healthcare yearly.
Leading strategies for prevention of hospital acquired infections
center around compliance with simple hygiene standards.
Varying degrees of hygiene compliance within small patient
networks are examined and compared across various network
topologies and resource availability. As expected, increased
hygiene compliance results in lower rates of infection
transmission, but increased resource availability paired with
simple homogeneous patient network architectures can lead to
highly accelerated transmission rates under certain conditions.
Alternatively, HAI can also emerge in the form of
bacterial infections resulting from hospital stays. One
such bacterial infection is known as the Clostridium
difficile Infection and has been linked to over 14,000
deaths in the USA each year. This infection causes
severe diarrhea and is closely associated with people
who receive medical care frequently [3]. Patients
become susceptible to the infection when taking
antibiotics, as these types of medications destroy all
types of bacteria including ones that aid in the body’s
immunity to disease and infection. During this time,
patients generally come into contact with the infection
through HCW that have neglected to wash their hands or
from surfaces (especially in healthcare facilities) that
have not been properly cleaned [4].
I. INTRODUCTION
Transmission and spread of hospital acquired
infections (HAI) is a major problem within hospitals in
the United States and is most often due to poor
compliance with essential, yet simple, hygiene standards
by hospital personnel. The U.S Department of Health
and Human Services (HHS) is the agency chiefly
responsible for collaborating with state and local
governments in an effort to protect the health of
Americans, most notably those who struggle to protect
themselves from illness [1]. Currently, the HHS has a
division focused solely on identifying the key factors
and risks associated with HAI spread throughout
medical facilities. This division of the HHS is known as
the Steering Committee for the Prevention of
Healthcare-Associated Infections. One of the central and
most common forms of infections within a hospital
environment occurs when a healthcare worker (HCW)
contaminates a central-line (otherwise known as an
umbilical or intravascular catheter) prior to insertion into
a patient, which ultimately results in a primary
bloodstream infection [2]. These types of infections are
more commonly referred to as central-line associated
bloodstream infections (CLABSI).
The two previously mentioned infections are two of
several that HHS has targeted in a recent campaign to
reduce the rates of HAI. Specifically, nine action items
have been identified as being central to the plan and are
currently being tracked, with goal metrics set to be
analyzed in 2013. Of the nine key metrics, several are
dedicated to the adherence to best-practice standards
concerning HCW hygiene in various hospital settings
[5].
Studying the affect that hygiene compliance has on
patient networks and infection transmission is vital to the
safety of patients nationwide and provides a reference
for compliance education. The campaigns established by
HHS illustrate the current and pressing need for better
understanding of hygienic practices in the medical
environment as well as higher compliance with existing
standards. Most importantly, this is a problem that could
106
potentially affect everyone who is ever in need of
medical care.
The model used in this experiment extends some
aspects of the previously described model.
Specifically, the following concepts have been either
extended or adapted to fit the parameters of this study:
Hospitals and medical care facilities should also have
a vested interest in the study and understanding of HAI
and how they are spread. Studies estimate that each
newly acquired infection causes healthcare costs to
increase by $12,197 and that yearly HAI can reach into
the tens of thousands in the USA alone [8].
A. Patient Network Topology
Similar to the previous model, this model assumes a
total network of patients, which represents a set of all
agents that are considered patients. The capacity of this
network is set before simulation starts and remains static
throughout the duration of the simulation. That is, no
patient can be introduced to nor leave the network after
simulation has started.
By the year 2013, HHS aims to have reduced CLABSI
by 50% and to have various hygiene standards in various
sectors of medical care adhered to 100% of the time.
Since most of these initiatives were started around 2006,
HHS can confidently say that they are on track to
achieve a majority of their goals by the deadline in 2013.
Despite being on track with metrics, HHS continues to
emphasize the importance of continuous education and
study in these areas [5].
The total network can also be broken down into
subsets, which we will refer to as patient groups. If there
is just one patient group present in the model, then the
total network is the patient group. As the number of
patient groups exceeds a single group, the total network
is split into n patient groups, each containing the same
capacity or near the same capacity should the capacity of
the total network be odd.
Whether the total network is split into subsets is based
on the number of available HCW resources. If there are n
available resources, the total network will then be split
into n subsets, each representing a patient group.
To study the issue of hygiene compliance, one must
not only model the compliance rate but also how HCW
interact with and among a network of patients. Studies
have shown that varying network topologies can have
drastic effects on the rate at which disease and infection
are spread [6], which is also true for hygiene
compliance. Together, both factors modeled together
may illustrate properties of infection transmission that
are crucial to the understanding and prevention of HAI.
II. METHOD
To examine the combined effects of varying patient
network topology and HCW resource allocation paired
with varying levels of HCW hygiene compliance, an
agent-based approach was utilized in creating a model
that can be considered synonymous with a small inpatient ICU. The concept for the model was adapted
from work done in studying transmission rates of
infections in varying patient networks in which
heterogeneous hospital HCW were shared amongst the
patient groups within the network. The rate of
transmission was then examined at varying levels of
network density and degrees of resources sharing [7].
The simulation tool used to run the model was
NetLogo.
Figure 1 illustrates the concept of a total patient
network that has been split into three equally sized
patient groups. Each group is represented by a different
color. Agents that are marked as red are HCW. In this
example, the total network has been split into three
patient groups because there are three available HCW.
Each HCW is assigned to a different patient group.
Fig 1: An example patient network having a total network
capacity of 30 patients and 3 patient groups, each with a
capacity of 10 patients each.
107
patients in the network depicted in Figure 1, each index
patient would be colored black. In this model, the color
black is reserved as a means of distinguishing index
patients and will never be used to represent a particular
patient group.
B. Infection Virulence
The virulence parameter used in the previous model
has been carried over into this model but has been
converted to a constant, used only to introduce another
level of stochasticity into the model. In these
experiments, the virulence is always set to 50% but can
be altered easily in the user interface.
Analogous to the virulence parameter, a new
parameter has been introduced, which serves to represent
the percentage chance of HCW complying with
workplace hygiene standards. Used on conjunction with
the virulence parameter, the chance of a patient
contracting an infection based on the virulence of the
infection and the hygiene compliance of his or her HCW
can be represented by:
E. Model Variables
The following variables represent the key points of
focus in the model’s behavior and can be directly
manipulated via the user interface:
1. NumberOfResources
• Represents the number of available HCW
in the model. The input for this variable
determines the number of patient groups
into which the total patient network will
be split (each available HCW is assigned
a patient group).
2. NumberOfPatients
• Represents the number of patients in the
total network as a whole. In other words,
the input for this variable determines the
patient count before the creation of
patient groups. The capacity of each
patient group after available HCW have
been taken into account will be roughly
NumberOfPatients
divided
by
NumberOfResources.
infection = virulence*hygieneCompliance
Equation 1
It is in this respect that the model developed for this
experiment differs from the previous model. Whereas
previously virulence was one of the main variances
studied, here we use hygiene compliance as the main
focus of study.
C. HCW Resource Allocation
The total number of available HCW resources is set
before simulation starts. The number of available
resources has a direct impact on what the patient network
topology will consist of during the simulation. Each
available HCW is assigned a patient group that has nearly
the same capacity as all other patient groups (if the
capacity of the total network is divisible by the number
of available HCW, each patient group is guaranteed to
have equal capacity to one another).
3. IndexPatientCount
• Represents the number of index patients
in each patient group. It is important to
note that the input for this variable does
not represent the total number of index
patients in the total network, but rather
the number of index patients in each
patient group. After setup, the total index
patients in the network as a whole would
*
be
(IndexPatientCount)
(NumberOfResources)
4. HygieneCompliance
• Represents the percentage chance of a
HCW complying with hygiene standards.
This variable can be freely manipulated at
runtime. The actual transmission
percentage is determined by both this
variable as well as Virulence.
5. Virulence
• Represents the percentage chance that the
particular infection in that’s present in the
network can spread from one patient to
another.
The
actual
transmission
In Figure 1, the available HCW are denoted by the
color red and can be seen standing beside the patient they
are each currently tending to. In this model, the color red
is reserved as a means of distinguishing HCW and will
never be used to represent a particular patient group.
D. Index Patients
A set number of index patients are established prior to
the start of the simulation. Index patients represent
patients in the network who are assumed to be already
infected at the start of the simulation. In this model, the
transmission of infection among each patient group is
able to be traced back to the one or many index patients
within each group. The patient groups depicted in figure
1 do not have index patients set. If there were index
108
percentage is determined by both this
variable as well as HygieneCompliance.
III. RESULTS
Results were obtained for 19 different parameter sets,
each representing 20 runs of the simulation. Virulence
remained constant at 50% in all of the runs so as not to
complicate the true effect of hygiene compliance on
infection transmission.
F. Model Behavior
1. Variables are assigned based on direct user input
via the user interface.
2. The total patient network is split into subsets of
patient groups based on the number of available
HCW.
3. Each patient is assigned to a patient group, as
evenly distributed as possible.
4. Each HCW is assigned to care for a patient group.
5. An initial number of index patients are
established in each patient group based on the
index patient count established by the user.
6. Each HCW initially chooses one patient to visit
7. On each successive time step, the model does the
following:
a. Each HCW picks a new random patient
(who wasn’t their last patient) to visit in
his or her patient group.
b. The HCW visits their new patient
c. A network link is created between the old
patient and the new patient.
d. If the last patient visited was infected, the
chance of the new patient becoming
infected is determined by Equation 1.
8. When all patients in the total network have been
infected, the simulation exists and reports the total
time steps to full infection of the network.
Table 1 summarizes the results obtained. Each row in
the table represents an average over 20 runs for the
parameters specified in that particular row. “Patient
Groups” represents the number of patient groups that
were created from the total network. This parameter can
also be thought of as the number of available HCW. “# of
Patients” represents the total number of patients in the
simulation. “# of Index Patients” represents the total
number of index patients in the network as a whole,
regardless of patient group assignments. “# of Index
Patients per Group” is an extension of the previous
parameter and makes clear how many index patients
were present in each patient group, as determined by user
input. “Hygiene %” represents the percentage that HCW
will comply with hygiene standards, as determined by
user input. Finally, “Average time steps to full infection”
represents the amount of time that it took for the entire
network to become infected. That is, the amount of time
it took for all patient groups to have no longer have a
healthy patient. This way, the average time to full
infection is analogous with the rate at which an HAI is
spreading across all patients in the total network.
Chart 1: Average time steps to full infection for a single patient
group with varying levels of capacity and hygiene compliance.
109
Interestingly, as the number of available HCW
resources increases, and as a result the number of patient
groups increases, the transmission rate of the HAI tends
to increase dramatically with each available resource.
Specifically, if the number of resources is doubled, it
seems that the average time to full infection is cut in half.
This can be clearly seen in Table 1. For example,
consider the simulation run in which there was only one
patient group with 50 patients and a hygiene compliance
of 25%. The average time to full infection for this
particular simulation was 846.35 time steps. Now
consider the simulation that has similar parameters,
except with double the patient groups (or double the
available resources). This would be the simulation with 2
patient groups, 50 patients, and a hygiene compliance of
25%. In that particular simulation, the average time to
full infection was 483.85 time steps, which is roughly
half of what was seen with only one patient group.
Similar data emerge for the same scenario with hygiene
compliance ratings of 50% and 75%.
Taking on this representation of spread rate, a
higher average time to full infection signifies a
lower rate of infection spread. If more time was
required to infect all patients, the infection must
have been spreading slower than a simulation which
had a lower average time to full infection. Using this
approach,
IV. DISCUSSION
As expected, the average time to full infection
was generally lower for simulation runs that had
lower hygiene compliance, as the HAI spread was
not prevented by a high frequency of hand washing
and other best-practice measures. Paired with this,
the average time to full infection was also lower
when the total patient count was low. This makes
sense, as fewer patients would take less time to
infect than a large number of patients. These
observations tend to support the hypothesis that
greater hygiene compliance generally leads to lower
rates of HAI transmission. Chart 1 emphasizes this
concept, showing that as the size of a network or
individual patient group increases, greater hygiene
compliance can have an increasing an exponential
effect on the transmission rate.
Patient Groups
# of Patients
# of Index Patients
# Index Patients Per
Group
Hygiene %
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
4
4
4
50
50
50
100
100
100
200
200
200
50
50
50
100
100
100
200
200
200
2
2
2
4
4
4
8
8
8
2
2
2
4
4
4
8
8
8
2
2
2
4
4
4
8
8
8
1
1
1
2
2
2
2
2
2
25
50
75
25
50
75
25
50
75
25
50
75
25
50
75
25
50
75
Table 1: Average time steps to full network infection for varying inputs.
Averages represent the average number of time steps over 20 runs.
110
Average time steps
to full infection
846.35
1414.30
3066.30
1830.95
3056.30
6272.05
4653.85
6507.90
13637.85
483.85
796.95
1494.90
969.25
1427.90
2953.50
1101.20
1817.00
3424.65
These observations seem to suggest that adding more
available resources to the network actually heightens the
rate at which the HAI is spread throughout the network
of all patients. Because of the way the model behaves, for
each available resource the total network is split into
subsets of near-equal patient groups. Since each HCW is
dedicated to its own network, and since the assumption is
held that all patient groups are nearly equal in every way
(capacity, index patient count, and only a single HCW) it
would make sense that the rate of HAI transmission
would become a parallel process within the total network.
In such a case, each patient group acts as its own isolated
total network since no HCW or patients can neither enter
nor exit a patient group at any time. If each patient group
is considered to be a parallel process within the total
network, it would then follow that the average time to
full infection for the network as a whole would roughly
become the average time to full infection of the
individual patient groups within the network.
networks that have not been broken into many patient
groups. As a large network is split into more and more
homogeneous patient groups, the spread of infection is
made parallel by each group and increases dramatically
across the network as a whole.
Results obtained in these experiments show promising
effects of high hygiene compliance and can be examined
further once HHS publishes their goal metrics in 2013.
Until then, medical facilities can use these results to
understand what patient network architectures should not
be used when attempting to prevent or stop the spread of
infection. That is, homogeneous patient groups that each
contains at least one or more initial index patients should
generally be avoided.
VI. FUTURE WORK AND EXTENSIONS
Admittedly, the model used in these experiments
behaves rather simply and makes many assumptions
about the state and topology of the complete patient
network. Given more time and further resources, these
assumptions could have been improved to reflect real
data and scenarios. Despite these assumptions, the model
builds a good foundation to additions and improvements.
The network topology that is assumed in the model
could be made more realistic by making the patient
groups heterogeneous. In a real setting, HCW may not all
be assigned patient groups with equal capacity.
Furthermore, one patient group may actually have
multiple HCW allocated to it, while another may only
have one HCW. Furthermore and most importantly,
different patient groups may contain a wide range of
index patients carrying a HAI. Some groups may not
even have an index patient. Such network characteristics
would have been difficult to model under the conditions
of this experiment, as the average time to full infection
for the network as a whole would simply approach
infinite if any one patient group contained no index
patients. Heterogeneous patient groups would more
closely resemble real scenarios and could be modeled
assuming alternative metrics are being collected.
Additionally, an interesting yet complex extension of
this model might vary the virulence parameter and see
how different levels of virulence may impact the
transmission rate. This parameter could also be used to
model specific HAI where strong data exists to suggest
that a generally known virulence rate can be used.
Finally, it would be interesting to examine strategies
for prevention of HAI transmission as the simulation
progresses. Dynamic patient groups and patient networks
would lend themselves nicely to developing a model that
Much like Amdahl’s Law postulates that the speedup
of a processor is directly related to the amount of the
program that can be made parallel and the number of
parallel processors that are available, the increase in HAI
transmission is directly related to the total number of
patients and the number of patient groups they are split
into (the patient groups act like parallel processors,
increasing the speed of transmission within the network
as a whole).
V. CONCLUSION
As the US Department of Health and Human Services
continues with their nine-point action plan to reduce the
occurrence of HAI in American medical facilities, the
importance of studying and understanding means of
prevention and factors of transmission is constantly
apparent. Thousands of deaths yearly and millions of
dollars could be saved by identifying strategies and
practices that reduce transmission rates among patients.
Most notably, rates of hygienic compliance have been
targeted as being vital to the reduction of HAI
transmission, especially within larger patient networks.
The vital nature of hygiene compliance was modeled
in NetLogo using a network of patients that was split into
equal parts according to the availability of healthcare
workers. Each subset was assigned the same number of
index patients, which are assumed to have an infection
from the start. Varying the degrees of HCW availability
as well as the hygiene compliance by HCW showed that
greater hygiene compliance can have promising returns
on reducing the rate of HAI transmission in large patient
111
adapts to newly acquired infections and strategically
forms alternative groups based on current HCW
availability and number of infected patients. Such an
approach could consist of a quarantine-like strategy for
prevention and eventual eradication of the HAI during
the simulation.
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