Modelling Market Dynamics and
Consumer Behaviour From The
Bottom Up
Iqbal Adjali
Mathematics & Informatics
Unilever R&D, Colworth Science Park
Bedford, UK
First ESSA Summer School
Brescia 15 September 2010
Unilever R & D
Consumer Modelling Research
Unilever – the Vitality Company!
Some Unilever Brands
Leading Categories & Brands
Foods
Home and Personal Care
Savoury & Dressings
Skin
Spreads
Deodorants
Weight Management
Laundry #1 in D&E
Tea
Daily Hair Care # 1 in D&E
World Number 1
Ice Cream
Household Care
World Number 2
Oral Care
Local Strength
Our 12 €1 billion brands
Feel Good, Look Good,
Get more out of life…
Mathematics & Informatics Group
Mathematics
Psychology
Personalisation Algorithms
Agent Based Methods
Network Science
Graphical Models
Consumer
Economics/Game Theory
Complexity
Behaviour Change Theory
Interactive Systems
Persuasive Technology
On-line Therapy
Natural Language Processing
Ubiquitous Computing
Connected Sensors
Computer Science
Agenda
Background and Motivation
● Marketing science – the legacy
● The social simulation approach to Marketing
● Challenges in applying social simulation to market and consumer
behaviour
Application Examples
● Modelling the diffusion dynamics of the trial patterns of an online
grocery store
● Break after 1h30mn?
● Modelling the volatility in market shares – A Micro-simulation
approach
● Social network interventions – Experimental study
● Social network interventions – ABM of the take-up of physical
exercise
General Discussion
Why is Understanding
Consumer Behaviour Important?
As an applied field, it’s relevant to:
● Business and market strategists
● Marketing managers/practitioners
● Market regulatory bodies
● Consumer groups
As a research discipline, it’s relevant to:
● Economics, sociology, psychology, anthropology,
biology
● Key to understanding human behaviour
Consumer Behaviour
Complexity and Emergence
● Unpredictability of market behaviour
(e.g. path dependence): Stochastic
behaviour of consumers
● Consumer-consumer interactions: e.g.
Word-of-Mouth dynamics
● Consumer lock-in phenomena: what
makes a new product successful
● Understanding and measuring the effect
of advertising / marketing interventions
Consumer Behaviour Literature:
Two Schools of Thought
● Economic theory
– Consumer behaviour is based on Demand
Theory and utility maximisation
– Purchase behaviour is a direct function of
external economic factors (price, income,...)
● Behavioural Sciences
– Internal and non-economic factors are
considered
– Based on statistical models
– Fragmented field
– Data driven
Consumer Behaviour:
Economic Approach
Rule for choice selection
Logit Model
pi  e
U i
n
e
U i
i 1
Ui utility of product i has for the consumer
● Traditional Theory of Demand
culminates in Lancaster’s Consumption
Technology Matrix
Kelvin Lancaster, “Consumer Demand: A New Approach”, Columbia University Press - NY, 1971
Consumer Behaviour
Economic Approach
● Advantages
– Mature theory - existence of consensus
– Amenable to quantitative modelling &
analysis
● Disadvantages
– Focuses on external economic factors
– Unrealistic assumptions (e.g. perfect
information, rationality)
– views consumer behaviour as the outcome
of the consumer decision process
Behavioural Sciences:
Some Approaches
Search and evaluation,
innovative behaviour,
change behaviour,
e.g. new product launch
Habitual behaviour,
e.g. influence of advertising
Theory of Planned
Behaviour
Stimulus-Response
Models
Post-purchase behaviour,
e.g. consumer
satisfaction/loyalty
Cognitive Dissonance
Theory
Influence of society on
decision process,
Social Network Theory
e.g. Word-of-mouth
Theory of Planned Behaviour
Outcome beliefs
Attitudes
Reference beliefs
Norms
Control beliefs
Perceived control
Predispositions
Attitudes
Intention
Motivations
F.M. Nicosia, Consumer Decision Processes, Prentice-Hall, 1966
Behaviour
Behaviour
Behavioural Sciences Approach
● Advantages
– takes into account internal (psychological)
and social and cultural factors
– more accurate in describing observed
behaviour
● Disadvantages
– No unified approach; disparate and often
conflicting models
– No formal models, statistical inference only
technique that can often be used
– Data difficult to get
Social Simulation
and Consumer Behaviour
Bottom-up modelling approach that allows one
to
● deal with consumers as individuals
● rules and mechanisms of arbitrary complexity
● take into account consumer-consumer
interactions
● consider time evolution/dynamics
Useful for both theory building and practical
applications
Forces researcher to develop formal frameworks
Social Simulation vs.
Traditional Methods
Relative Merits
Agent-Based Modelling
Traditional Methods
Bottom-up (disaggregate)
Consumers as individuals
Top-down (aggregate)
Representative Consumer
Market discontinuities (emerging
structure)
Stable Markets (given structure)
Explicit Modelling of Social Networks
No easy way to model SN
Evidence-based, general (non-Normal) Single-valued or Normally distributed
distribution of variables
variables
Integrated Framework
Separate Models
Key Challenges for
Consumer Behaviour Modelling
● Data availability/gathering
● Standardised model building approaches –
for comparison/duplication
● Model testing/validation methodologies
Model Validation
PREDICTION
Model Validation refers to the
process of selecting the right model
to match observations with
predictions, given model complexity.
Validation increases both insight
and prediction.
Model complexity acts as the
constraint on the whole exercise.
INSIGHT
● Model validity is crucial for our purposes, as a robust agent based
simulation will be one based on a validated MODEL, giving GOOD
PREDICTIONS, and providing USEFUL INSIGHTS
Validation Approaches
● K-I-S-S (Keep It Simple Stupid)
● Quantitative (Fagiolo, 2005; Werker, 2004; Windrum, 2007)
– Numerical techniques to search parameter space efficiently
– Model calibration with macro AND micro level observations
– Use of optimization techniques like GA/GP/ANT/SWARM
● Qualitative (Garcia, 2007)
– History friendly approach
– Based more on expert opinions and stylized facts
– Draws heavily from established theory
● Experimental (Richetin et. al. 2009 and our ongoing collaboration)
– Uses in-situ human players to run experiments
– Simulation designed to mimic experiment OR experiments designed to
test simulation
– Hybrid approach using quantitative, qualitative and experimental styles
– Cutting edge interdisciplinary
Advancing Consumer Behaviour
Research
● Investigate impact of advanced psychological
theories on consumer behaviour
● Investigate role of social networks and context
dependency in determining consumer behaviour
● Design controlled experiments (e.g. to test wordof-mouth dynamics, effect of advertising,…)
● Closer collaboration across disciplines and
between academia and industry
A Spatio-temporal Agent Based
Model of Consumer Trials of a Swiss
Online Grocery Store
Modelling the diffusion of
a new consumer service
● Context & Motivation
● Diffusion dynamics
– Bass, ABM
● Data
– The LeShop database
● Model Specification
● Simulation results
● Conclusion
Introduction
Background
● Diffusion dynamics is an important concept in Marketing and
the modelling of markets
● Different approaches have been used in the literature
(aggregate, disaggregate, statistical,…)
● Difficulty in getting the right data for the right approach
Motivation
● Data available: individual-based customer transactions from the
online grocery supermarket (LeShop) and geo-statistical data
● Develop an empirically motivated ABM
● Opportunity to integrate an ABM in a spatial (geographical) context
● Research question*: Do neighbourhood effects play an
important role in the spatio-temporal dynamics of information
diffusion?
*Bell, D. and Song, S. (2004). Social contagion and trial on the internet: Evidence from online grocery retailing.
Working paper, Wharton School Marketing Department.
Modelling Diffusion: Bass
● Bass Diffusion Model*
– Top-down (aggregate) model
– Global variables/parameters
– Has been successful in predicting market take-up of
innovations in consumer durables
– Not easily generalisable (to many products and many
competitors)
– Restrictive assumptions (e.g. homogeneous population,
perfect mixing…)
*Bass, F., “A new product growth model for consumer durables”, Management Science 15(5), 1969
Shopper and Market Data
ABM Platform
Transaction
data
Customer
transaction
data
GIS/demo
data
Office of
Swiss Stats
Quality
data
Marketing
Agencies
Advertising
data
Marketing
Agencies
Data Description
Customer
data
GIS/demo
data
Three Linked Datasets:
● Customers, Transactions, Products (1998-2003)
Customer Table (~4.5k):
● UserID,ZIP_Code,Age_Range,Gender,Language
Transaction Table (~2m) :
● User_ID,Basket_ID,Purchase_Date_Time,SKU_Number,Pri
ce,Quantity,Discount
Product Table (~10k):
● SKU_Number$Category$Sub_Category$Brand_ID$Quality
Cumulative trials by language
Monthly trials by language
The Swiss District Postcode Map
GIS census data
The Customer Agents
Social Networks
Recommendation diffusion
2000
2001
● We looked at the diffusion
of the recommended
membership
(Only components with at
least 9 members are taken
into account)
2002
2003
2004
2005
● 2002-2004 remarkable
increase in “horizontal”
connectivity – people
started to react earlier,
recommendations are taken
during the same year
Recommendation network
Age distribution
15-17y
18-24y
25-34y
35-44y
55-64y
● Again, we analyse
only components
with more than 9
members!
● Notable absence of
older generations
early on in the
recommendation
patterns!!
Recommendation network:
Gender and geographical distribution
whole network
AG
Family
7%
ZH
Male
33%
GE
Female
60%
VS
Families have a big role in
recommendation scheme!
VD
NE
recommendation network
FR
Family
17%
OTHER
Intercantonal connections which surpass language barriers
are due to Lausanne – Zurich connection and to “small”
cantons.
Female
57%
Male
26%
Agent Behaviour
The only endogenous variable in agents is the trial
state: Aij. It evolves according to the following rule:
•If Aij=0 then invoke the external influence rule:
: random number drawn from
uniform distribution [0,1]
•If Aij still =0 then invoke the internal influence rule:
•Implement a small world network for social interactions
Simulation Results
● We performed several hundred simulation runs,
sweeping the parameter space (F,G,F,G).
● We calibrate the model on the real aggregate trial
data by maximising Goodness-of-fit according the
LOESS algorithm.
● This procedure led to the following calibrated
parameter values:
Cumulative Customer Trials
Real vs. Simulated Trials
French
German
Goodness of fit – LOESS Statistics
R2
0.63
0.52
0.64
Degree
4.2
4.5
4.3
Spatio-Temporal Diffusion
Each customer agent is unique and reacts to:
Global Communication and
Word of Mouth interactions
French
ABM
German
Prob. to adopt due global influences (α)
0.001
0.0007
Prob. to adopt due to local interactions (β)
0.125
0.085
Monthly Customer Trials
Merger with Migros
(Janurary 2004)
Actual
Promotional Campaigns
Cumulative Total Customers
I. Adjali et al, (2007) “An Agent Based Model of Customer Tirials in an
Online Grocery Store", presented at: ABM Marketing Conference,
Groningen, 22 August 2007
Conclusion (Innovation Dynamics)
● A social simulation approach to marketing does make
sense: it is a very effective way to capture:
– Market and consumer heterogeneity
– Consumer interactions
● Comparison with real data is a crucial step in
validating the model (aggregate and individual levels)
● Neighbourhood (spatial) effects do exist and seem to
matter even in online markets
– Useful to consider the spatial dimension explicitly
when appropriate
● Challenges: explore parameter space, macro vs. micro
validation, look at different diffusion processes e.g.
product launches, opinion dynamics…
What Social Simulation Means
For The Marketing Discipline
● Computational modelling of
individual consumer
behaviour, social networks
and brand relationships
leads to better insight in
consumer behaviour and
market dynamics
● Enhance predictive power
of marketing mix models
● develop robust marketing
strategies through detailed
scenario analyses
Volatility in the Consumer Packaged
Goods Industry – A Micro-Simulation
Based Study
In collaboration with
Nigel Gilbert and Alan Roach, Surrey University
Frank Smith and Stephen Glavin, UCL
Partly published in: Sengupta et al., Advances in Complex Systems 2010
Introduction
● Consumer goods markets
– Characterised by noisy market share dynamics and
instability (Jager: 2007)
– Heterogeneous consumers with wide variety of
tastes/preferences (Allenby, Rossi: 1998)
– Intense competitive interventions from multiple firms
using pricing, promotions, advertising etc. (Ailawadi
et. al.: 2001, Blattenberg, Wisniewski: 1989).
● Additionally, social networks, WoM may play important
roles
Consumer Strategies
● Each strategy filters the list of available products.
● The final choice is selected randomly from any remaining.
● Available strategies
–Cheapest – with a noise parameter on perceived difference.
–Brand Loyalty – choose the brand it has bought most in the
past.
–Threshold – selects products below its predefined
maximum price.
–Change of pace – will swap brand after a number of weeks,
defined by a parameter.
Assessment
● To evaluate runs,
– The difference between the actual monthly sales for
each brand and the simulated sales data is
calculated.
– Each brand’s overall fitness is the sum of all the
monthly differences.
– And the model’s fitness is the sum of all the brands’
overall fitnesses.
● Quite crude, but we are looking for a rough fit.
● This is then used to assess the fit of models under
different parameters settings.
Parameter Exploration
● Two aspects of tuning, parameters and strategies.
● Even with this simple model there are a lot of possible
variations – 61,440!
● A subgroup of 17 strategy combinations was identified.
● So two sweeps were done.
– A broad sweep to identify best strategy combinations
and parameters.
– A fine tuning sweep to identify the best parameter
settings for these strategies.
Charts of best runs
40
40
35
35
30
30
25
25
20
20
15
15
10
10
5
5
0
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43
Target Sales
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43
Threshold Fitness 307
Charts of best runs
40
40
35
35
30
30
25
25
20
20
15
15
10
10
5
5
0
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43
Target Sales
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43
Threshold, Change of
pace, Brand Loyalty,
Cheapest. Fitness 343
Conclusions
● The search process identified models which roughly replicated
the data.
● The best model for these data is the simplest one, Threshold.
● But other combinations were fairly successful.
● Overall the main weakness was not modelling the late sales
peak of the red product.
● This is a prototype process for assessing the success of
consumer strategies for modelling our data.
Fruit Juice Category dynamics
● Traditional approaches – Logit and Probit models
(Frances, Paap:2001; Anderson et. al.: 1992).
● General focus is on the effects of promotions on quantity,
incidence and market structure over a short term (Chan:
2008).
● They are generally independent of time and ignore the
dynamics .
● Fail to examine the effects of heterogeneity at the
individual level on market dynamics.
● Lack non-linearities such as social interactions (Jager:
2007).
● Predictions at the individual level not possible.
● Poor out-of-sample performance.
DATA
• Transactions from Swiss online supermarket from
January 2006 to December 2006 (52 weeks)
• Fresh fruit juice category
• Each transaction included
– Household ID
– Individual Product (SKU) ID
– Week number
– Net price paid
– Discount received
– Quantity of product purchased
DATA FILTERING
● Eliminate households who purchase infrequently
 55 SKUs, 2435 households, 28179 transactions.
● Data is divided into three temporal partitions
– Week 1-24: To be used in initialisation.
– Week 25-38: To be used for calibration.
– Week 38-52: To be used for out of sample prediction.
● Three dominant characteristics in products chosen – brand,
flavour, pack size.
PRODUCT FEATURES
Brand
No. of Products
Flavour
No. of Products
Isola
2
Kid’s Drink
3
Danone
2
Grape Fruit
2
Mickey’s Adventures
2
Nectar
7
Oasis
1
Pineapple
2
Capri Sonne
2
Apple
11
Granini
5
Multi-fruit
12
Michel
5
Orange
12
Obi
2
Other fruit
6
Nectar
8
Hohes C
4
Ramseier
5
Max Havelaar
1
Actilife
3
M
8
Gold
5
Total
55
55
MODEL
● Have industry with K distinct products and a consumer base of size
N.
● Each product has M attributes that make it unique for a consumer –
defining an address vector for the product in characteristic space.

X k  x1k , xk2 ,...,xkM

● Each consumer has a preference – a vector of characteristics that
they would like to see in a product; their ideal point.
i  1i , i2 ,...,iM 
● The closer the ideal point is to the address of a product, the higher
the subjective utility for the consumer from purchasing it.
MODEL

The utility from product k to agent i :


Ui k   i dki  1   i pk

dki Normalized relative distance of product from ideal point
Dki
d 
max Dki
i
k


pk Net price of k
i
jK
Individual specific single parameter
M
D   | xki  kj |
i
k
j 1
VALIDATION
– Initialisation
• Product characteristic vectors and agent ideal points are
initialised within 3-d characteristics space
– Calibration
• Agent level calibration carried out at both micro and macro
level.
– Testing
• Carried out at both micro and macro level.
• Parameterised agents used to make out of sample
predictions
• Monte-Carlo type simulation using multiple runs where each
corresponds to a random draw from the optimised parameter
set of each agent. (100 runs per agent)
• A market share based random model used as benchmark for
comparison of our model
MODEL TEST RESULTS
● Macro Validation
– Comparison of predicted and actual market shares of
brands and flavours with predicted and actual percentages.
– Two measure used:
• Mean weekly relative difference between actual and
simulated market shares per brand/flavour
• Correlation coefficient.
– Volatility in market shares is captured very well.
– Small price changes (promotions in flavours) result in high
levels of volatility which is captured in our model
– Significantly outperforms the benchmark
PREDICTED AND ACTUAL WEEKLY MARKET SHARES BY BRAND
MODEL TEST RESULTS
● Micro Validation
– Measure accuracy of predictions for
household specific choice of products AND
characteristics in each dimension separately
– Measure joint predictions along subsets of
dimensions.
– The model works very well at the individual
level as well as aggregate level.
– Individual level prediction of characteristic
choice accuracy is superior over product
choice accuracy
– Results significantly outperforms the
benchmark
SUMMARY
● Bottom-up simulation developed to model fruit juice
market using loyalty card checkout data for empirical
validation.
● Agents using simple behavioural model initialised and
calibrated using part of the data with predictions tested
against remaining data
● Heterogeneity within consumers’ tastes and preferences
and price responsiveness
● High levels of out-of-sample prediction achieved at both
aggregate and disaggregate household level.
SUMMARY
● Weekly evolution of product groups with medium to large
market shares overall predicted to high degree
– Slightly better in terms of direction of change over
magnitude
● Micro-level: model predicted accurately every SKU purchase
for 35% of transactions.
● Brands and flavour choice captured with high degree of
accuracy.
● Volatility in market shares captured without the addition of
“noise” factors.
● The benchmark model without heterogeneity fails to achieve
same levels of accuracy
ON GOING AND FUTURE RESEARCH
● Test our model on other data sets.
● Restrict rationality in agents decision making. Add
cognitive elements.
● Introduce changing preferences, changing attitudes,
changing social norms.
● Incorporate social feedbacks and peer pressure
effects.
● Adapt modelling framework for longer term analysis,
introducing technology changes, entry exit etc.
Social Network Interventions
In Consumer Markets
In Collaboration with:
Marco Perugini & Juliette Richetin, University of Milan Bicocca
Alex Linley, Centre for Applied Positive Psychology, UK
To be part published in Greetham et al.
Proceedings of Applications of Social Network Analysis Conference, 2010
Background 1
Research on the spread of
obesity, smoking
(Christakis& Fowler
2007, 2008) and
happiness (Fowler &
Christakis 2009) based
on Framingham heart
study data shows
evidence of social
network influence on
long term dynamics.
Background 2
•
Network Spread of Obesity?
 Clusters of obese people (1971 - 2003)
 Chances of becoming obese increased by
57% if had friend who became obese.
 40% if adult sibling became obese
 37% if spouse
 No effect of geographic neighbour
 Greater influence from same sex
• Network Spread of Happiness?
 Clusters of happy and unhappy people
 Influence up to 3 degrees of separation
 Chances of becoming happy increases by
25% if near-by friend becomes happy
 8% for spouse
 14% sibling
 34% next door neighbour
 No effect between co-workers
Advantage of a Network/ABM Approach
– Modelling Irrationality
• Richetin et al (2009). A Micro Level Simulation for the Prediction
of Intention and Behavior, Cognitive Systems Research
 Compared to standard statistical approach the agent-based simulation generally
improved the prediction of behaviour from intention
 The improvement in prediction is inversely proportional to the complexity of the
underlying theoretical model
 The introduction of varying degrees of deviation from rationality in agents’
behaviour can lead to an improvement in the goodness of fit of the simulations
 Future work could focus on conflicting goals (CG), discrepancy (goal – actual) &
Effort
Network Mechanisms
Study Design
• Pilot Study to Map Transfer of ‘Positivity’ with CAPP





20 Participants in second year university course.
Plus a minimum of 5 people in their network
Equals 20 egos and 100 alters [120 nodes and the ties between]
Complete daily measures for 14 days
Agent based modelling of transfer within network over time
• Baseline Measures






Specify others in network: reciprocity of friendship
Personality: (Gosling et al, 2003)
Trait Gratitude: GQ-6 (Emmons & McCullough, 2003)
Trait Emotional Intelligence: (Petridis & Furnham, 2001)
Trait Positive and Negative Affect: PANAS (Watson, Clark, & Tellegen, 1988)
Satisfaction with Life: (Diener, Emmons, Larsen, & Griffin, 1985).
• Daily Measures





Daily frequency of interaction with others in network
Type of interaction with others in network: Proximal - Distal
Valence of interaction
Daily levels of positive and negative affect
Daily influences on well-being
Design
● Baseline: gender, age, ethnicity, big 5
personality traits, grattitude score
● Daily measures: PANAS, sleep, general health
● Contacts – mode, valence, duration
● Post-hoc social network
Objectives
I.
II.
To analyse short term dynamics of happiness
contagion
To identify causal mechanisms by which
happiness spreads
Positive and negative affect (independent constructs)
PANAS – Positive Affect Negative Affect Schedule
Covariates
● Age, gender, ethnicity
● Personality: 5 traits
Agreeableness, Conscientiousness, Emotional
stability, Extroversion, Openness to experience
● Grattitude score
Siena
● Simulation Investigation for Empirical Network Analysis
● Actor-based models
● Iterative stochastic simulation algorithm updating
parameters
● Expected values approximated as averages over
simulated networks
● Observed values are target values
http://www.stats.ox.ac.uk/~snijders/siena/
PA&NA
General health & Sleep
Post-hoc Network
Social Network Snapshots
PA and NA
NA
http://www.stanford.edu/group/sonia/
Results - PA, NA
Selection process:
Actors with higher value of NA would increase
no. contacts more rapidly.
Influence process:
Different shapes:
PA - push toward the midpoint of range,
negative feedback
NA - push to extremes
Results - personality traits
● Emotional stability has positive effect on sleep and
health and negative on NA
● Extraversion has positive effect on PA
● Openness to experience similarity: actors prefer ties
to others with similar value
● Actors with higher values of openness
tend to increase their out-degree more rapidly
● But opposite for extraversion!
Results related to gratitude and sleep
● Grattitude has positive effect on NA rate,
and negative on sleep rate
● Sleep effect from ethnicity negative and from emotional
stability positive
● Sleep influence – push to midpoint range
Summary
● PA&NA have different mechanisms of influence
● Personality traits (esp. emotional stability and openness
to experience)
have effect on PA, NA, general health and sleep
● Grattitude scores have effects on NA and sleep rate
Effect of peer pressure on individual
behaviour – Simulating the case of
physical activity with an Agent Based
Model
(with a view to applying the approach to
behaviour change interventions)
Presented by A. Sengupta at the WCSS conference in Kassel, Sep 2010
1
What this talk is about…
● Can my friends cure me of my laziness?
Goal Directed Behavior
• Ajzen, 1991
• Perugini & Conner, 2000
• Perugini & Bagozzi, 2001
Goal
Formation
Intention
What neighbours are
doing…
Physical
Activity
Recycling
Preparing for
exam…
Behavior
Tasks, Influence and Behaviour
● Role of the environment on individual motivation
– Stahl, Rutten, Nutbeam, Soc. Sc. Med, 2001
– Giles-Corti, Donovan, Soc. Sc. Med., 2002
– Giles-Corti, Donovan, Am. J. of Soc. Health, 2003
– McNeill, Wyrwich, Brownson, An. of Beh. Med.,
2006
– Zoethout, Jager, Molleman, JASS, 2006
Questions
● What are the emergent patterns of behavior within
groups under influence of both internal and external
factors?
● What is the nature of interaction between internal and
external factors?
● Does the nature of external influence have an effect on
behavioral outcomes?
Generate hypotheses using ABM simulations which can
be tested experimentally.
Extend the framework to incorporate other goal directed
behaviors as well.
Models
● Model 1
– Goal directed motivation (actual vs. ideal state)
– Goals constant over time
– Observance of positive and zero behavior in
neighbours (dual threshold model)
● Model 2
– Shifting goals for some (optimizers vs. satisfiers)
– Opportunity cost of behavior
– Habit formation from repeated behavior
External Influence
● Network topologies
– Erdos-Renyi Random Network ER(n,m)
– Barabasi Scale Free B(n,d)
– Watts-Strogatz Small World WS(s,d,p)
– Empirical: Newman PNAS, 2006
● Network influence
– “Dual” threshold model
– Upper threshold  2
– Lower threshold 1

0


V (t )   B


 B(t)

n
 1
N
n
if
 2
N
if
otherwise
Simulation Setup
●
●
●
●
●
●
Netlogo environment
379 agents (empirical network driven)
Ideal state ~ U[80, 120], Actual state ~ U[50, 150]
B ~ # of hours per week
Time step ~ 1 week
Theoretical networks
– ER (379, 914), B(379, 3), WS(7, 3, 0.4)
● Parameters tested in Model 1
 ~ (0,6)
1 ~ (0,1)
 2  1
Results (Model 1)
No Networks
No Networks: Benchmark
1. There exists a critical value of rho around which the average properties of
the system change
2. Increasing rate of physical decay leads to more physical activity on average
Results (Model 1)
With Networks
1.
Average Behavior fails to
reach the maximum.
2.
A critical value of rho exists
around which the average
steady state behavior of the
system changes.
3.
Low rho: expected behavior
4.
High rho: unexpected
behavior in (ideal – actual)
(a)  2  0.9;   3.5
(b)  2  0.9;   4.5
Frequency
(c)  2  0.6;   3.5
(d)  2  0.6;   4.5
Model 2
●
●
Introducing Optimizers and Satisfiers
– Optimizers: Readjusts goal
– Satisfiers: Constant goal
Behavior depends on ideal-actual
discrepancy and opportunity cost
B(t )  Kd (t )  opp.cost(t)
●
Opportunity cost of positive behavior
c(t )  [ B  B(t )]exp[0.5B(t )]
●
Habit formation due to repeated behavior
c' (t )  [ B  A  B(t )]exp[0.5B(t )]  A
Opportunity
Cost
Opportunity
Cost
Repeated Behavior
Behavior
Behavior
Results (Model 2)
No Networks
Small World
Random
Scale Free
Results (Model 2)
● No Network case:
– Avg behavior is strictly decreasing in prop. of
satisfiers and strictly increasing in B.
– Avg opp. cost is strictly increasing in prop. of satisfiers
and strictly decreasing in B.
– Avg motivation is weakly decreasing in prop. of
satisfiers.
Results (Model 2)
● With Networks
– Avg behavior and motivation energy fall, and avg opp.
cost rise significantly in presence of networks.
– Patterns of change of avg behavior and opp. cost is
preserved when compared to benchmark.
– But avg motivation is now a strictly decreasing
function of prop of satisfiers.
Conclusion
● In a closed system with individual goals, observations
from peers is more likely reduce behavior – increase
laziness.
● Amount of behavior can decrease but frequency may
increase if internal motivation is high enough.
● Introducing habit formation does not improve the
situation if networks are present.
● Type of network does not make a significant qualitative
difference.