1. 2 plan of the course u introduction u rules of encounters u strategic negotiation u auctions s...
TRANSCRIPT
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2
Plan of the course
Introduction Rules of Encounters Strategic Negotiation Auctions
protocolsstrategies
Argumentation
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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
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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)
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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
AT&TAT&TAT&TAT&TMCIMCIMCIMCI SprintSprintSprintSprint
$0.20$0.20$0.23$0.23
$0.18$0.18
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Attributes of the Mechanism
Distributed Symmetric Stable Simple Efficient
AT&TAT&TAT&TAT&TMCIMCIMCIMCI SprintSprintSprintSprint
$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
AT&TAT&TAT&TAT&TMCIMCIMCIMCI SprintSprintSprintSprint
$0.20$0.18$0.18 $0.23$0.23
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Attributes of the Mechanism
Distributed Symmetric Stable Simple Efficient
AT&TAT&TAT&TAT&TMCIMCIMCIMCI SprintSprintSprintSprint
$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.
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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”.
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Fax Domain
faxes tofaxes tosendsenda
cb
d e
f
Cost isCost isonly toonly to
establishestablishconnectionconnection
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TODTOD
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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
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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?
Post OfficePost Office
2
1
11
11 22
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–1 Phase Game: Broadcast Tasks
Agents will flip a coin to decide who delivers all the letters.
a
c
bh
f d
g
e
Post OfficePost Office
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
Post OfficePost Office
((11))
11 22
ee
bb
2
1
ff
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Another Possibility for Deception
a
c
bThey will agree to flip a
coin to decide who goes to b and who goes to c.
Post OfficePost Office
b, cb, c
2
1
b, cb, c
11 , ,22
11 , ,22
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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
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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
Post OfficePost Office
((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
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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..
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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
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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�
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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
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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.
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Environment Description
serveri serverj
a query
document/s
area iarea j
distance
a client
the document/s
the query
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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.
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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.
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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).
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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.
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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.
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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).
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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.
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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.
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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.
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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.
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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.
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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.
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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
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.
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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
Number of Pollutions
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
Number of Pollutions
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
Number of Pollutions
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.
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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>.
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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.