Automated Negotiation

1

2

Plan of the course

Introduction Rules of Encounters Strategic Negotiation Auctions

protocolsstrategies

Argumentation

3

Machines Controlling and Sharing Resources

Electrical grids (load balancing) Telecommunications networks (routing) PDA’s (schedulers) Shared databases (intelligent access) Traffic control (coordination)

4

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

5

Attributes of Standards

Efficient: Pareto Optimal Stable: No incentive to deviate Simple: Low computational and

communication cost Distributed: No central decision-maker Symmetric: Agents play equivalent roles

Designing protocols for specific classes of domains Designing protocols for specific classes of domains that satisfy some or all of these attributesthat satisfy some or all of these attributes

Designing protocols for specific classes of domains Designing protocols for specific classes of domains that satisfy some or all of these attributesthat satisfy some or all of these attributes

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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

Distributed Artificial Intelligence (DAI)

7

Phone Call Competition Example

Customer wishes to place long-distance call Carriers simultaneously bid, sending proposed prices Phone automatically chooses the carrier (dynamically)

AT&TAT&TAT&TAT&TMCIMCIMCIMCI SprintSprintSprintSprint

$0.20$0.20$0.18$0.18 $0.23$0.23

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Best Bid Wins

Phone chooses carrier with lowest bid Carrier gets amount that it bid


$0.20$0.20$0.23$0.23

$0.18$0.18

9

Attributes of the Mechanism

Distributed Symmetric Stable Simple Efficient


$0.20$0.20

$0.18$0.18 $0.23$0.23

Carriers have Carriers have an incentive an incentive

to invest to invest effort in effort in

strategic strategic behaviorbehavior

“Maybe I can bid as

high as $0.21”...

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Best Bid Wins, Gets Second Price

Phone chooses carrier with lowest bid Carrier gets amount of second-best price


$0.20$0.18$0.18 $0.23$0.23

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Attributes of the Mechanism

Distributed Symmetric Stable Simple Efficient


$0.20$0.20

$0.18$0.18 $0.23$0.23

Carriers have Carriers have nono incentive incentive

to invest to invest effort in effort in

strategic strategic behaviorbehavior

“I have no reason to

overbid”...

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Database Domain

Common DatabaseCommon Database

“All female employeeswith more than three

children”.2

1

TODTOD

“All female employees

making over $50,000 a

year”.

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NegotiationNegotiation

“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

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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 decision-maker’s actions on the other participants is not taken into consideration.

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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.

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Example of two players game

dindia

Dsikh deal

deal

blow

op

1

2

0

2 -3 -

0

2 -

1 -

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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.

18

c

0.6

0.4

Ind

Indop

op-3,0-

2,1-

dealH

dealH

sik

sik

sik

sikdealH

dealH

blow3,-5

2,52,1-

blow

yes

yes3,4

Ind

Ind

dealH

dealH

op

op

1,4

1,4

4, -4

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Rules of Encounter

Jeffrey S. RosenscheinJeffrey S. RosenscheinGilad ZlotkinGilad Zlotkin

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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

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Postmen Domain

Post OfficePost Office

a

c

d e

21

TODTOD

b

f

22

Database Domain

Common DatabaseCommon Database

“All female employeeswith more than three

children”.2

1

TODTOD

“All female employees

making over $50,000 a

year”.

23

Fax Domain

faxes tofaxes tosendsenda

cb

d e

f

Cost isCost isonly toonly to

establishestablishconnectionconnection

21

TODTOD

24

Slotted Blocks World

11 22 33

11 22 33

SODSOD

2

1

25

The Multi-Agent Tileworld

2 22

2

55

34

AB tiletileholehole

obstacleobstacle

agentsagents

WODWOD

26

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 An encounterencounter is a list T is a list T11 ,…, T ,…, Tnn of of finite sets of tasks from finite sets of tasks from TT such such

that agent that agent AAkk needs to achieve all needs to achieve all the tasks in Tthe tasks in Tkk (also called agent (also called agent

AAkk’s ’s goalgoal))..

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Building Blocks

DomainA precise definition of what a goal isAgent operations

Negotiation ProtocolA definition of a dealA definition of utilityA definition of the conflict deal

Negotiation StrategyIn EquilibriumIncentive-compatible

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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)

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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…

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Building Blocks

DomainA precise definition of what a goal isAgent operations

Negotiation ProtocolA definition of a dealA definition of utilityA definition of the conflict deal

Negotiation StrategyIn EquilibriumIncentive-compatible

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Negotiation with Incomplete Information

a

c

bh

f d

g

e What if the agents don’t know each other’s letters?


2

1

11

11 22

32

–1 Phase Game: Broadcast Tasks

Agents will flip a coin to decide who delivers all the letters.

a

c

bh

f d

g

e


11

11 22

2

1

ee

b, fb, f

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Hiding Letters

They then agree that They then agree that agent 2 delivers to agent 2 delivers to

f and ef and e..

((hiddenhidden))

a

c

bh

f d

g

e


((11))

11 22

ee

bb

2

1

ff

34

Another Possibility for Deception

a

c

bThey will agree to flip a

coin to decide who goes to b and who goes to c.


b, cb, c

2

1

b, cb, c

11 , ,22

11 , ,22

35

Phantom Letter

b, c, b, c, ddPost OfficePost Office

2

1

b, cb, ca

c

b 11 , ,22

11 , ,22 d11( ( phantomphantom))

They agree that agent 1 goes to c.

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Negotiation over Mixed Deals

TheoremTheorem: With mixed : With mixed deals, agents can deals, agents can

always agree on the always agree on the “all-or-nothing” deal“all-or-nothing” deal

Mixed deal (D1, D2) : p

The agents will perform (D1, D2) with probability p, and the symmetric deal (D2, D1) with probability 1 – p

37

Hiding Letters with MixedAll-or-Nothing Deals

They will agree on the mixed deal where agent 1 has a 3/8 chance of delivering to f and e.

((hiddenhidden))

a

c

bh

f d

g

e


((11))

11 22

ee

bb

2

1

ff

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Phantom Letters with Mixed Deals

They will agree on the mixed deal where A has 3/4 chance of delivering all letters, lowering his expected utility.

a

c

b

b, c, b, c, ddPost OfficePost Office

2

1

b, cb, c

11 , ,22

11 , ,22 d11( ( phantomphantom))

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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)

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Sub-Additivity

cc(X (X Y) Y) cc(X) + (X) + cc(Y)(Y)

XX YY

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Sub-Additive TODs

The Postmen Domain, Database Domain, and Fax Domain are sub-additive.

The “Delivery Domain” )where The “Delivery Domain” )where postmen don’t have to return to the postmen don’t have to return to the

Post Office( is not sub-additivePost Office( is not sub-additive..

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Incentive Compatible Mechanisms

Sub-AdditiveSub-Additive

a

c

b 11 , ,22

11 , ,22 d((phantomphantom))11

((hiddenhidden))

a

c

bh

f d

g

e

((11))

11 22

TheoremTheorem: For all encounters in all sub-: For all encounters in all sub-additive TODs, when using a PMM over all-additive TODs, when using a PMM over all-

or-nothing deals, no agent has an incentive or-nothing deals, no agent has an incentive to hide a taskto hide a task..

Hidden

Pure L L

A/N T T/P

Mix L T/P

Phantom

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Decoy Tasks

Sub-AdditiveSub-AdditiveHidden

Pure L LA/N T T/PMix L T/P

Phantom

LLL

Decoy

Decoy tasks, Decoy tasks, however, can be however, can be

beneficial even with beneficial even with all-or-nothing dealsall-or-nothing deals

11

11

11 11

22

2211

44

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-Concavity implies sub-additivityadditivity..

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Concavity

XXYY

ZZ

The cost Z adds to X is more than the cost it adds to Y.

(Z - X is a superset of Z - Y)

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Concave TODs

The Database Domain and Fax Domain are concave (not the Postmen Domain, unless restricted to trees).

11

11

11 11

22

2211X

Z

This example was not concave; Z adds 0 to X,

but adds 2 to its superset Y (all blue

nodes).

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Three-Dimensional Incentive Compatible Mechanism Table

Sub-AdditiveSub-AdditiveHidden

Pure L LA/N T T/PMix L T/P

Phantom

LLL

Decoy

ConcaveConcaveHidden

Pure L LA/N T T

Mix L T

Phantom

LT

T

Decoy

TheoremTheorem: For all : For all encounters in all encounters in all

concave TODs, when concave TODs, when using a PMM over all-using a PMM over all-

or-nothing deals, no or-nothing deals, no agent has any agent has any

incentive to lieincentive to lie..

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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 Modularity implies concavityconcavity..

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Modularity

c(X Y) = c(X) + c(Y) – c(X Y)

XX YY

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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 Even in modular TODs, hiding tasks can be beneficial in tasks can be beneficial in

general mixed dealsgeneral mixed deals..

51

Three-Dimensional Incentive Compatible Mechanism Table

Sub-AdditiveSub-Additive

Pure

A/N

Mix

ConcaveConcave

Pure

A/N

Mix

H

L LT T

L T

P

LT

T

D

H

L LT T/PL T/P

P

LLL

D

ModularModular

Pure

A/N

Mix

H

L T

T T

L T

P

T

T

T

D

52

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

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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 Rules of EncounterEncounter

Rules of Rules of EncounterEncounter

EfficiencyEfficiencyEfficiencyEfficiency

54

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

StabilityStabilityStabilityStability

Formal Formal ToolsToolsFormal Formal ToolsTools

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Strategic Negotiation

Collaborators: Jon Wilkenfeld, Rina Schwartz-Azoulay, Orna Shechter, Esti Freitsis

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DAI Overview

AI

DAI

DPS MA

strategic negotiation

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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.

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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

equidistant iterations 0,1,2 …־Time and can continue forever. In each time period

t, agent j(t) =t mod N makes an offer .

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Structure of the Negotiation - cont.

The other agents respond simultaneously: YES or NO or OPT.If the offer was accepted by all the agents:

the last offer is implemented.If at least one agent opts out:

a conflict occurs.Otherwise (the offer was rejected by at least

one agent), the negotiation proceeds to period t+1. ֲ ֱא�

60

Applications

Information servers (large databases). Resources sharing. Tasks distribution. Computer assisted negotiation. Union/management negotiation.

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Negotiation on data allocation in multi-server

environment

62

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.

63


serveri serverj

a query

document/s

area iarea j

distance

a client

the document/s

the query

64

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 of new datasets arrive.

65

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.

66

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).

67

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.

68

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 theservers. The set of all possible allocation is denoted by Allocs.

U: the utility function of each server.

69

The Conflict Allocation

If at least one server opts out 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).

70

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)= Vserver(x,alloc(x)). x־DATASETS

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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.

72

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.

73

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.

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Equilibrium

Nash equilibrium:A strategy profile p is a Nash Equilibriumif 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.

75

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 subgame-perfect equilibrium of the bargaining game, with the outcome x offered and unanimously accepted in period 0.

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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:(Us(x)-Us(conflict)).

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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 allocationthe allocation which maximizes the predefined

social welfare criterion will be chosen.

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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.

79

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.

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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 significantly, but vcost_ratio decreases as the standard deviation of the usage increases.

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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 vcost_ratio ס. storage_cost ס vcost_ratio ס. retrieve_cost ס vcost_ratio ע.query_price ס vcost_ratio ע.

82

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.

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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.

84

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.

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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.

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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.

87

Negotiations in the pollution sharing problem

Collaborator: Esti Freitsis

88


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.

89

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.

90

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.

91

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.

92

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).

93

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.

94

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.

95

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.

96

Techniques which were checked

Strategic negotiations:Sequential responses: backtrackingSimultaneous 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

97

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.

98

Plants’ utility as the function of the number of plants

0

100

200

300

400

500

600

700

800

900

5 10 15 20

Number of Plants

Uti

lity

pe

r P

lan

t

Max Sum

Praxis

Alt. offers

Hill climbing

99

Standard Deviation as the function of the number of plants

0

50

100

150

200

250

300

350

400

450

5 10 15 20

Number of Plants

Sta

nd

art

De

viat

ion

of

Uti

litie

s

Max Sum

Praxis

Alt. offers

Hill climbing

100

Computation time as a function of number of plants

0.1

1

10

100

1000

10000

5 10 15 20

Number of Plants

Tim

e

Max Sum

Praxis

Alt. offers

Hill climbing

101

Plants’ utility as the function of the number of pollution substances

0

50

100

150

200

250

300

350

400

450

500

5 10 15 20

Number of Pollutions

Uti

lity

pe

r P

lan

t

Max Sum

Praxis

Alt. offers

Hill climbing

102

Standard deviation as the function of the number of pollution substances

0

50

100

150

200

250

300

350

400

450

500

5 10 15 20


Sta

nd

art

De

viat

ion

of

Uti

litie

s

Max Sum

Praxis

Alt. offers

Hill climbing

103

Computation time as a function of the number of pollution substances

0.1

1

10

100

1000

5 10 15 20


Tim

e

Max Sum

Praxis

Alt. offers

Hill climbing

104

Plants’ utility as a function of the number of products

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5 10 15 20

Number of Products

Uti

lity

pe

r P

lan

t

Max Sum

Praxis

Alt. offers

Hill climbing

105

Standard deviation as a function of the number of products

0

500

1000

1500

2000

2500

3000

3500

4000

5 10 15 20

Number of Products

Sta

nd

art

De

viat

ion

of

Uti

litie

s

Max Sum

Praxis

Alt. offers

Hill climbing

106

Computation time as the function of the number of products

0.1

1

10

100

1000

5 10 15 20


Tim

e

Max Sum

Praxis

Alt. offers

Hill climbing

107

Computation time as a function of the number of products

0.1

1

10

100

1000

5 10 15 20

Number of Products

Tim

e

Max Sum

Praxis

Alt. offers

Hill climbing

108

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.

109

Sharing Resources Through Negotiation

Joint resource: public communication system; satellite;

Agents: self motivated.

Environment: no central controller.

110


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>.

111

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.

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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).

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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.

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Experiments Using MINUET

Agent 1 Agent 2

Working on goal 102####

Send request <5,3>

Receive request <5,3>

Resources1001 - free1002 - busy

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Experiments Results

Nego. EDFMetricUtility score 91% 91%Abandon goals 9.6 8.4Nego./Alter. 21.2 15.5

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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;

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Summary--cont.

The model was applied to different domains. We found simple and stable strategies. Negotiation ends without delay.

Documents

Automated Negotiation