1
Plan of the course
 Introduction
 Rules
of Encounters
 Strategic Negotiation
 Auctions
 protocols
 strategies
Argumentation
2
Machines Controlling and
Sharing Resources
 Electrical
grids (load balancing)
 Telecommunications
networks (routing)
 PDA’s
(schedulers)
 Shared
databases (intelligent access)
 Traffic
control (coordination)
3
Broad Working Assumption
 Designers
(from different companies,
countries, etc.) come together to agree on
standards for how their automated agents
will interact (in a given domain)
 Discuss various possibilities and their
tradeoffs, and agree on protocols,
strategies, and social laws to be
implemented in their machines
4
Attributes of Standards
Efficient:
 Stable:
 Simple:
Pareto Optimal
No incentive to deviate
Low computational and
communication cost
 Distributed: No central decision-maker
 Symmetric: Agents play equivalent roles

Designing protocols for specific classes of domains
that satisfy some or all of these attributes
5
Distributed Artificial Intelligence
(DAI)
 Distributed
Problem Solving (DPS) —
Centrally designed systems, built-in
cooperation, have global problem to solve

Multi-Agent Systems (MAS) —
Group of utility-maximizing heterogeneous
agents co-existing in same environment,
possibly competitive
6
Phone Call Competition
Example
 Customer
wishes to place long-distance call
 Carriers simultaneously bid, sending proposed prices
 Phone automatically chooses the carrier (dynamically)
MCI
AT&T
$0.20
$0.18
Sprint
$0.23
7
Best Bid Wins
 Phone
chooses carrier with lowest bid
 Carrier gets amount that it bid
MCI
AT&T
$0.20
$0.18
Sprint
$0.23
8
Attributes of the Mechanism
Distributed
 Symmetric
 Stable
 Simple
 Efficient

Carriers have an
incentive to
invest effort in
strategic
behavior
MCI
“Maybe I
can bid as
high as
$0.21...”
$0.18
AT&T
$0.20
Sprint
$0.23
9
Best Bid Wins, Gets Second
Price
 Phone
chooses carrier with lowest bid
 Carrier gets amount of second-best price
MCI
AT&T
$0.20
$0.18
Sprint
$0.23
10
Attributes of the Mechanism
Distributed
 Symmetric
 Stable
 Simple
 Efficient

Carriers have no
incentive to
invest effort in
strategic
behavior
MCI
“I have no
reason to
overbid...”
$0.18
AT&T
$0.20
Sprint
$0.23
11
Database
Domain
TOD
“All female
employees
making over
$50,000 a
year.”
Common Database
“All female
employees
with more
than three
children.”
2
1
12
Negotiation
“A discussion in which interested parties
exchange information and come to an
agreement.” — Davis and Smith, 1977
Two-way
exchange of information
Each
party evaluates information from
its own perspective
Final agreement is reached by mutual
selection

13
Game Theory--Short Introduction
Game theory is the study of decision making in
multi-person situations where the outcome depends
on everyone’s choice.
 In Decision Theory and the theory of competitive
equilibrium from economics the other participants
actions are considered as an environmental
parameter. The effect of the of the decisionmaker’s actions on the other participants is not
taken into consideration.

14
Describing a Game
 Essential
elements: players, actions,
information, strategies, payoffs, outcome, and
equilibria.
 Ways to present social interactions as a game:
 Extensive form:the most complete description.
 Strategic form: many details are omitted.
 Coalitional form: binding agreements exist.
15
Example of two players game
india
d
deal
sikh
D
blow
op
deal
1
0
2
2-
23-
1-
0
16
Nash Equilibrium
 An
action profile is an order set
a=(a1,…,aN) of one action for each of the N
players in the game.
 An action profile a is a Nash Equilibrium
(Nash 53) of a strategic game, if each agent
j does not have a different action yielding an
outcome that it prefers to that generated
when chooses aj, given that every other
player I chooses ai.
17
op
Ind
3-,5 blow
sik yes
2,5
2,1blow yes
sik
dealH
0.4
c
0.6
Ind
op
2,1-
dealH
dealH
sik
dealH
3,4
op
Ind
dealH
Ind
dealH
sik
op
-3,0-
4- ,4
1,4
1,4
18
Rules of Encounter
Jeffrey S. Rosenschein
Gilad Zlotkin
19
Domain Theory
Task
Oriented Domains
 Agents have tasks to achieve
 Task redistribution
State Oriented Domains
 Goals specify acceptable final states
 Side effects
 Joint plan and schedules
Worth Oriented Domains
 Function rating states’ acceptability

Joint plan, schedules, and goal relaxation
20
Postmen Domain
Post Office
1
TOD
2
a

c
b


d

f

e
21
Database
Domain
TOD
“All female
employees
making over
$50,000 a
year.”
Common Database
“All female
employees
with more
than three
children.”
2
1
22
Fax Domain
2
1
TOD
faxes to
send
a
c
b
f
d
Cost is
only to
establish
connection
e
23
Slotted Blocks World
SOD
1
3
2
1
2
1
2
3
24
The Multi-Agent Tileworld
WOD
agents
hole
B
A
tile
22
2
5
5
obstacle
2
34
25
Task Oriented Domain (TOD)
A tuple < T, A, c > where:
 T is the set of all possible tasks
•
A = A1 , … , An is a list of agents
• c is a monotonic function c : [2T ]  +
An encounter is a list T1 ,…, Tn of finite sets
of tasks from T such that agent Ak needs
to achieve all the tasks in Tk (also called
agent Ak’s goal).
26
Building Blocks



Domain
 A precise definition of what a goal is
 Agent operations
Negotiation Protocol
 A definition of a deal
 A definition of utility
 A definition of the conflict deal
Negotiation Strategy
 In Equilibrium
 Incentive-compatible
27
Deal and Utility in two-agent
TOD
 Deal
 is a pair (D1, D2): D1  D2 = T1 
T2
 Conflict
deal:  = (T1, T2)
 Utilityi()
= Cost(Ti) – Cost(Di)
28
Negotiation Protocols
 Agents
use a product-maximizing
negotiation protocol (as in Nash
bargaining theory);
 It
should be a symmetric PMM (product
maximizing mechanism);
 Examples:
1-step protocol, monotonic
concession protocol…
29
Building Blocks



Domain
 A precise definition of what a goal is
 Agent operations
Negotiation Protocol
 A definition of a deal
 A definition of utility
 A definition of the conflict deal
Negotiation Strategy
 In Equilibrium
 Incentive-compatible
30
Negotiation with Incomplete
Information
Post Office
1
h
a
g
f

1
b

1
2
c
e

2
d
What if the agents
don’t know each
other’s letters?31
–1 Phase Game: Broadcast
Tasks
Post Office
b, f
h
a
b
1

e
1
2
g
f

1
c
e

2
d
Agents will flip a
coin to decide
who delivers
32
all the letters.
Hiding Letters
Post Office
f
h
a

1
b

e
(1)
(hidden)
g
f
b
1
2
c
e

2
d
They then agree that
agent 2 delivers to
f and e.
33
Another Possibility for
Deception
Post Office
b, c
1
b, c
2
a
c
b

1, 2

1, 2
They will agree to flip
a coin to decide who
goes to b and who
34
goes to c.
Phantom Letter
Post Office
a
b, c, d
1
b, c
2
c
b

1, 2

1, 2

d
1 (phantom)
They agree that
agent 1 goes to c.
35
Negotiation over Mixed
Deals
Mixed deal (D1, D2) : p
The agents will perform (D1, D2)
with probability p, and the
symmetric deal (D2, D1) with
probability 1 – p
Theorem: With mixed deals,
agents can always agree on
the “all-or-nothing” deal
36
Hiding Letters with Mixed
All-or-Nothing Deals
Post Office
f
h
a

1
b

(1)
(hidden)
g
f
b
1
e
2
c
e

2
d
They will agree on the
mixed deal where agent
1 has a 3/8 chance of
delivering to f and e. 37
Phantom Letters with Mixed Deals
Post Office
a
b, c, d
1
b, c
2
c
b

1, 2

1, 2
They will agree on the mixed
deal where A has 3/4
chance of delivering all
d
letters, lowering his
expected utility.
38
1 (phantom)

Sub-Additive TODs
TOD < T, A, c > is sub-additive if for all
finite sets of tasks X, Y in T we have:
c(X  Y)  c(X) + c(Y)
39
Sub-Additivity
X
Y
c(X  Y)  c(X) + c(Y)
40
Sub-Additive TODs
The Postmen Domain, Database Domain, and
Fax Domain are sub-additive.


The “Delivery Domain” (where
postmen don’t have to return to the
Post Office) is not sub-additive.
41
Incentive Compatible
Mechanisms
a
h
a
g
f

1
b
c
e

(1)
(hidden)
b
Sub-Additive
d
Hidden Phantom

2
c
Pure
A/N
Mix
L
T
L

1, 2

1, 2

d
1 (phantom)
L
T/P
T/P
Theorem: For all encounters in all sub-additive TODs,
when using a PMM over all-or-nothing deals, no agent
has an incentive to hide a task.
42
Decoy Tasks
Decoy tasks, however,
can be beneficial even
with all-or-nothing deals
1
1
Sub-Additive
Hidden Phantom Decoy
Pure
L
A/N
T
Mix
L
L
T/P
T/P
L
L
L


1


1
1

2

2
43
Concave TODs
TOD < T, A, c > is concave if for all finite sets
of tasks Y and Z in T , and X  Y, we have:
c(Y  Z) – c(Y)  c(X  Z) – c(X)
Concavity implies sub-additivity.
44
Concavity
Z
Y
X
The cost Z adds to X is more than the
cost it adds to Y.
(Z - X is a superset of Z - Y)
45
Concave TODs
The Database Domain and Fax Domain are
concave (not the Postmen Domain, unless
restricted to trees).
Z
1
X
1
 2
1
2


1
1
This example was not concave;
Z adds 0 to X, but adds 2 to its
superset Y (all blue nodes).
46
Three-Dimensional Incentive
Compatible Mechanism Table
Theorem: For all encounters
in all concave TODs, when
using a PMM over all-ornothing deals, no agent has
any incentive to lie.
Concave
Hidden Phantom Decoy
Pure
L
L
L
A/N
T
T
T
Mix
L
T
T
Sub-Additive
Hidden Phantom Decoy
Pure
L
A/N
T
Mix
L
L
T/P
T/P
L
L
L
47
Modular TODs
TOD < T, A, c > is modular if for all finite
sets of tasks X, Y in T we have:
c(X  Y) = c(X) + c(Y) – c(X  Y)
Modularity implies concavity.
48
Modularity
X
Y
c(X  Y) = c(X) + c(Y) – c(X  Y)
49
Modular TODs
The Fax Domain is modular (not the Database
Domain nor the Postmen Domain, unless
restricted to a star topology).
Even in modular TODs, hiding tasks can
be beneficial in general mixed deals.
50
Three-Dimensional Incentive
Compatible Mechanism Table
Modular
Concave
H
Sub-Additive
H
Pure
A/N
Mix
P
D
L L
T T/P L
L T/P L
P
D
Pure
L
L
L
A/N
T
T
T
Mix
L
T
T
H
P
D
Pure
L
T
T
A/N
T
T
T
Mix
L
T
T
L
51
Related Work
Coalitions Formations: Shehory, Sandholm
 Mechanism design:Ephrati, Kraus, Tennenholtz
 Other models of negotiation: Sycara, Durfee,
Lesser, Gasser, Gmytrasiewicz, Jennings
 Consensus mechanisms, voting techniques,
economic models: Ephrati, Wellman, Sandholm

52
Conclusions
 By
appropriately adjusting
the rules of encounter by
which agents must interact,
we can influence the private
strategies that designers build
into their machines
 The interaction mechanism
should ensure the efficiency
of multi-agent systems
Rules of
Encounter
Efficiency
53
Conclusions
 To
maintain efficiency over
time of dynamic multi-agent
systems, the rules must also be
stable
 The use of formal tools
enables the design of efficient
and stable mechanisms, and
the precise characterization of
their properties
Stability
Formal
Tools
54
Strategic Negotiation
Collaborators: Jon Wilkenfeld, Rina SchwartzAzoulay, Orna Shechter, Esti Freitsis
55
DAI Overview
AI
DAI
DPS
MA
strategic negotiation
56
Strategic Negotiation Model
 Model
of alternative offers (Rubinstein)
which takes negotiation time into
consideration: reduces negotiation time.
 During the strategic-negotiations agents
communicate their respective desires to
reach mutually beneficial agreement.
 The model provides a unified to many
problems.
57
Structure of the Negotiation
There are N self motivated agents, randomly
designated 1,2,...
All the agents negotiate to reach an 
agreement.
The negotiation process may include several
Time ‫־‬equidistant iterations 0,1,2…
and can continue forever. In each time
period t, agent j(t) =t mod N makes an
offer.


58
Structure of the Negotiation - cont.

The other agents respond simultaneously:
YES4 or NO8 or OPTM.



If the offer was accepted4 by all the agents:
the last offer is implemented.
If at least one agent opts outM:
a conflict occurs.
Otherwise (the offer was rejected8 by at least
one agent), the negotiation proceeds to period
t+1.ֱ‫ֲא‬
59
Applications
Information servers (large databases).
 Resources sharing.
 Tasks distribution.
 Computer assisted negotiation.
 Union/management negotiation.

60
Negotiation on data
allocation in multi-server
environment
61
Environment Description
 There
are several information servers. Each
server is located at a different geographical
area.
 Each server receives queries from the clients
in its area, and sends documents as
responses to queries. These documents can
be stored locally, or in another server.
62
Environment Description
the query
serveri
a query
distance
document/s
server
j
the document/s
a client
area i
area j
63
Environment Description - cont.
 The
information is clustered in datasets
(corresponding to file, fragment, etc.)
 Each new dataset has to be allocated to one
of the servers by mutual agreement among
the servers.
 Each server wants to store the datasets in a
location which reduces its communication
and storage costs.
 A negotiation session is initiated when a set
64
of new datasets arrive.
Motivation
 Cooperation
among servers with similar
areas of interest (e.g., Web servers).
 The Data and Information System
component of the Earth Observing System
(EOSDIS) of NASA:
A distributed knowledge system which
supports archival and distribution of data at
multiple and independent servers.
65
Motivation - cont.
 Each
data collection, or file, is called a
dataset. The datasets are huge, so each
dataset has only one copy.
 The current policy for data allocation in
NASA is static: old datasets are not
reallocated; each new dataset is located by
the server with the nearest topics (defined
according to the topics of the datasets stored
by this server).
66
Related Work File Allocation Problem
The original problem:
How to distribute files among computers, in
order to optimize the system performance.
Our problem:
How can self-motivated servers decide
about distribution of files, when each server
has its own objectives.
67
Basic Definitions
SERVERS:
the set of the servers.
 DATASETS:
the set of datasets (files) to be allocated.
 Allocation:
a mapping of each dataset to one of the
servers. The set of all possible allocation is denoted
by Allocs.


U: the utility function of each server.
68
The Conflict Allocation
at least one server opts outM of the
negotiation, then the conflict allocation
conflict_alloc is implemented.
 We consider the conflict allocation to be the
static allocation. (each dataset is stored in
the server with closest topics).
 If
69
Utility Function
 Userver(alloc,t)
specifies the utility of server
from alloc‫־‬Allocs at time t.
 It consists of


The utility from the assignment of each dataset.
The cost of negotiation delay.
Userver(alloc,0)= S
Vserver(x,alloc(x)).
x‫־‬DATASETS
70
Parameters of utility
query price: payment for retrieved
docoments.
 usage(ds,s): the expected number of
documents of dataset ds from clients in the
area of server s.
 storage costs, retrieve costs, answer costs.

71
Cost over time
Cost of communication and computation time of
the negotiation.
 Loss of unused information: new documents can
not be used until the negotiation ends.
 Datasets usage and storage cost are assumed to
decrease over time, with the same discount ratio
(p-1).

 Thus,
there is a constant discount ratio of
the utility from an allocation:
Userver(alloc,t)= t*Userver(alloc,0) - t*C.
72
Assumptions
 Each
server prefers any agreement over
continuation of the negotiation indefinitely.
 The
utility of each server from the conflict
allocation is always greater or equal to 0.
 OFFERS
- the set of allocations that are
preferred by all the agents over opting out.
73
Equilibrium
 Nash
equilibrium:
A strategy profile p is a Nash Equilibrium
if no player has a different strategy yielding
an outcome that he prefers to that generated
when it chooses pi.
 Subgame Perfect Equilibrium:
If the strategy profile induced in every
subgame is a Nash Equilibrium of this
subgame.
74
Negotiation Analysis Simultaneous Responses
 Simultaneous
responses:
A server, when responding, is not informed
of the other responses.
 Theorem:
For each offer x ‫ ־‬OFFERS, there is a subgameperfect equilibrium of the bargaining game, with
the outcome x offered and unanimously accepted in
period 0.
75
Choosing the Allocation
 The
designers of the servers can agree in
advance on a joint technique for choosing x:
 giving each server its conflict utility.
 maximizing a social welfare criterion:

the sum of the servers’ utilities.

or the generalized Nash product of the servers’
utilities:
P (Us(x)-Us(conflict)).
76
Choosing the Allocation - cont.
 The
problem of finding an optimal
allocation is NP-complete (a reduction from
the multiprocessors scheduling).
 When finding x is intractable, we suggest
the following protocol:


each server will search for an allocation
the allocation which maximizes the predefined
social welfare criterion will be chosen.
77
Search Methods

We have implemented the following algorithms:

A backtracking algorithm:
Searching the search space of the allocation problem.

A random restart hill-climbing algorithm:
Starts with a random allocation and tries to improve it.

A genetic algorithm:
Searching by simulating an evolution process. Each
individual represents an allocation. The algorithm
involves: reproduction, crossover and mutation of
individuals.
78
Experimental Evaluation

How do the parameters influence the results of the
negotiation?
 vcost(alloc): the variable costs due to an
allocation (excludes storage_cost and the gains due
to queries).
 vcost_ratio: the ratio of vcosts when using
negotiation, and vcosts of the static allocation.
79
Effect of Parameters on The
Results
 As
the number of servers grows, vcost_ratio
increases (more complex computations) .
 As the number of datasets grows,
vcost_ratio decreases (negotiation is more
beneficial) .
 Changing the mean usage did not influence
vcost_ratio significantlyK, but vcost_ratio
decreases as the standard deviation of the
usage increases.
80
Influence of Parameters - cont.
When the standard deviation of the distances
between servers increases, vcost_ratio decreases.
 When the distance between servers increases,
vcost_ratio decreases.
 In the domains tested,





answer_cost ‫ס‬
storage_cost ‫ס‬
retrieve_cost ‫ס‬
query_price ‫ס‬
vcost_ratio ‫ ס‬.
vcost_ratio ‫ ס‬.
vcost_ratio ‫ ע‬.
vcost_ratio ‫ ע‬.
81
Social Criteria
 We
studied the effect of the choice of the
social welfare criterion on the results.
 We compare the following criteria:


Sum of agents’ utilities.
Product of agents’ utilities.
 Maximizing
the sum achieves lower
vcost_ratio.
 Maximizing the product achieves lower
dispersion of the agents’ utilities.
82
Incomplete Information
 Each


server knows:
The usage frequency of all datasets, by clients
from its area.
The usage frequency of datasets stored in it, by
all clients.
83
Incomplete Information - cont.
 A revelation

mechanism:
First, all the servers report simultaneously all
their private information:
– for each dataset, the past usage of the dataset by this
server.
– for each server, the past usage of each local dataset
by this server.

Then, the negotiation proceeds as in the
complete information case.
84
Incomplete Information - cont.
 Lemma:
There is a Nash equilibrium where each
server tells the truth about its past usage of
remote datasets, and the other servers usage
of its local datasets.
 Lies
concerning details about local usage of
local datasets are intractable.
85
Summary: negotiation on data
allocation
We have considered the data allocation problem in
a distributed environment.
 We have presented the utility function of the
servers, which expresses their preferences.
 We have proposed using a negotiation protocol for
solving the problem.
 For incomplete information situations, a revelation
process was added to the protocol.

86
Negotiations in the pollution
sharing problem
Collaborator: Esti Freitsis
87
Environment Description





There are some closely grouped plants in an industrial
region.
Each plant can produce several types of products.
Each plant has a utility function (profit).
There are several types of pollution substances.
Each plant has norms, restricting maximal emission of each
polluting substance that it emits. The pollution always has
to be below these norms. We refer to the situation when
only these norms have to be carried out as usual
circumstances.
88
Special circumstances
 Sometimes
there is a need to reduce
pollution for some period because of
external factors such as weather (high
humidity, wind towards residential
area). In this case plants receive new norms.
We refer to this situation as special
circumstances.
89
Current solution
 Current
solution: each plant reduce pollution
according to the new norms.
 Disadvantage: for one plant it is less costly
to reduce one substance while for another it
is less costly to reduce another substance.
90
Negotiations
 Our
solution: plants negotiate to reach
beneficial agreements about the emission of
what substances and by which percent each
of them must be reduced.

The conflict solution: following the new norms.
 We consider complete information situations.
91
Negotiations Protocols
 Simultaneous
responses:
an agent responding to an offer is not
informed of the other responses.
 Sequential responses: an agent responding
to an offer is informed of the responses of
the preceding agents (assuming that the
agents are ordered).
92
Negotiations strategies for
simultaneous responses
 As
in the data allocation case:
 For each possible agreement x that is better
to all the plants than the conflict solution
there is a subgame-perfect equilibrium of the
bargaining game, with the outcome x offered and
unanimously accepted in period 0.
93
Negotiations strategies for
sequential responses


Assumption: there is a time period, T where negotiation
cannot continue anymore. In T the conflict allocation is
implemented.
Perfect equilibrium by backward induction:



At T-1 if negotiations hasn’t ended, AT-1 suggests the best
agreement to itself which is better to all agents than the conflict
solution (denoted by OT-1 ); the other agents accept.
At T-2, AT-2 suggests the best agreement to itself which is better to
all agents than the conflict solution and OT-1 (denoted by OT-2). The
other agents accept.
By induction, at the first time period A0 O0 the others accept.
94
Assumptions about the environment
 Profit
is a linear function of the number of
items of each product produced by the plant
 Pollution is a linear function of the number
of items of each product produced.
95
Techniques which were checked
 Strategic negotiations:


Sequential responses: backtracking
Simultaneous response: Maximization of the sum
with guaranties of default profit :
– Simplex method - method for linear
optimization
 Nash Product:
 Praxis - method for multi-variable nonlinear
function minimization.
 Hill Climbing
96
Simulation Parameters
Number of plants is varied from 5 to 20.
 Number of pollution types is varied from 5 to 20.
For each product pollution of some type is
produced with probability 1/2.
 Each plant produces Max_prod different types of
products. Max_prod is varied from 5 to 20.
Pollution and profit per item of product and
pollution constraints are set randomly.


Results: Average of 25 simulation runs.
97
Plants’ utility as the function of
the number of plants
98
Standard Deviation as the
function of the number of plants
99
Computation time as a function of
number of plants
100
Plants’ utility as the function of the
number of pollution substances
101
Standard deviation as the function of
the number of pollution substances
102
Computation time as a function
of the number of pollution substances
103
Plants’ utility as a function of the
number of products
104
Standard deviation as a function of
the number of products
105
Computation time as the function of
the number of products
106
Computation time as a function of
the number of products
107
Conclusions
Maximizing the sum yields the highest average
utility, but also the highest standard deviation;
requires agreement between the designers on
selecting a solution.
 Backward induction yields a reasonable average
utility with low standard deviations and no need
for designers agreement on detailed protocol.
 On going work: incomplete information.

108
Sharing Resources Through
Negotiation
Joint resource: public communication
system; satellite;
Agents: self motivated.
Environment: no central controller.
109
Environment Description
 Two
agents must share a joint resource; the
resource can only be used by one agent at a
time. No central controller.
 One agent (A) is using the resource, and the
second (W) wants to use it too.
 The agents negotiate to reach an agreement:
a schedule that divides the usage of the
resource; <s,t>.
110
Environment Description -cont
 A continues
to use the resource as the
negotiation proceeds: A gains over time.
 W is not able to use the resource: W loses
over time.
 Opting out causes damage to the resource:
both agents wait q time steps.
 Additional option: an agent can leave the
negotiation.
111
Applying the strategic model
 We
developed a detailed utility function for
the agents (U_A; U_W).
Parameters: type of goal, dead-lines, costs of
negotiation, gains from goal, etc.
 Main
factor in the negotiation: the best
agreement for A, which is still better for W
than Opting out (O_n).
112
Perfect equilibrium strategies
 O_n
depends on the specific situation;
we proved lemmas which specify the value
of O_n as a function of the utility function
parameters.
 Complete information: Negotiation ends at
most after one step with an agreement, or W
leaves.
 The strategies are simple.
113
Experiments Using MINUET
Agent 1
Working on goal 102
Agent 2
Send request <5,3>
####
Receive request <5,3>
Resources
1001 - free
1002 - busy
114
Experiments Results
Metric
Utility score
Abandon goals
Nego./Alter.
Nego.
91%
9.6
21.2
EDF
91%
8.4
15.5
115
Summary
 A strategic
model of negotiation, taking the
passage of time into account.
 We consider wide range of situations:
complete /incomplete information;
N>2 agents;
agents lose over time/some lose and some
gain over time;
116
Summary--cont.
 The
model was applied to different domains.
 We found simple and stable strategies.
 Negotiation ends without delay.
117