Upload
others
View
3
Download
1
Embed Size (px)
Citation preview
Negotiation
Negotiation
Jose M Vidal
Department of Computer Science and Engineering University of South Carolina.
March 3, 2010
Abstract
We describe automated negotiation as it applies to multiagentsystems. Chapter 6.
Negotiation
Introduction
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Introduction
Why Negotiate?
Coordinate selfish interests.
Aggregate distributed conflicting knowledge.
Solve characteristic form games and more complex versions.
For example: NASA missions, capitol hill?
Negotiation
Introduction
Why Negotiate?
Coordinate selfish interests.
Aggregate distributed conflicting knowledge.
Solve characteristic form games and more complex versions.
For example: NASA missions, capitol hill?
Negotiation
The Bargaining Problem
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
The Bargaining Problem
Bargaining Problem
ui : ∆→ < where ∆ is the set of deals.
δ− is the no-deal deal.
Assume that for all agents ui (δ−) = 0
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Pareto
Definition (Pareto optimal)
A deal δ is Pareto optimal if there is no other deal such thateveryone prefers it over δ. That is, there is no δ′ such that
∀iui (δ′) > ui (δ).
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Pareto Frontier
ui (δ)
uj(δ)
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
What do we want?
We will want a Pareto deal, but which one?
Idea: Come up with some requirements first then see if asolution that meets those requirements exists.
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
What do we want?
We will want a Pareto deal, but which one?
Idea: Come up with some requirements first then see if asolution that meets those requirements exists.
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Independence from Units
Definition (Independence of utility units)
A negotiation protocol is independent of utility units if when givenU it chooses δ and when given U ′ = {(β1u1, . . . , βI uI ) : u ∈ U} itchooses δ′ where
∀i ui (δ′) = βiui (δ).
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Symmetry
Definition (Symmetry)
A negotiation protocol is symmetric if the solution remains thesame as long as the set of utility functions U is the same,regardless of which agent has which utility.
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Individual Rationality
Definition (Individual rationality)
A deal δ is individually rational if
∀i ui (δ) ≥ ui (δ−).
Which means that ui (δ) ≥ 0 since we will be assuming thatui (δ
−) = 0. A deal is individually rational if all the agents prefer itover not reaching an agreement.
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Independence from Irrelevant Alternatives
Definition (Independece of irrelavant alternatives)
A negotiation protocol is independent of irrelevant alternatives if itis true that when given ∆ it chooses δ and when given ∆′ ⊂ ∆where δ ∈ ∆′ it again chooses δ, assuming U stays constant.
That is, a protocol is independent of irrelevant alternative is thedeal it chooses does not change after we remove a deal that lost.Only removal of the winning deal changes the deal the protocolchooses.
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Egalitarian
δ = arg maxδ′∈E
∑i
ui (δ′)
where E is the set of all deals where all agents receive the sameutility, namely
E = {δ | ∀i ,jui (δ) = uj(δ)}.
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Egalitarian Social Welfare
Find the closest approximation:
δ = arg maxδ
mini
ui (δ)
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Egalitarian
ui (δ)
uj(δ)
y = x
Egalitarian deal
Egalitarian social welfare deal
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Utilitarian Solution
δ = arg max∑
i
ui (δ).
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Utilitarian Solution
ui (δ)
uj(δ)
y = x
Utilitarian deal
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Nash Bargaining Solution
δ = arg maxδ′
∏ui (δ
′).
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Nash Bargaining Solution
ui (δ)
uj(δ)
y = x
Nash bargaining deal
1
5
10
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Nice Nash
Nash bargaining solution is the only one that satisfies:
1 Pareto efficient
2 Independent of utility units
3 Independent of irrelevant alternatives
4 Symmetric
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Kalai-Smorodinsky
Let u∗i be the maximum utility that i could get from the set ofall deals in the Pareto frontier.
Then, find the deal that lies in the line between the point δ−
and the point (u∗i , u∗j )
Negotiation
The Bargaining Problem
Axiomatic Solution Concepts
Kalai-Smorodinsky
ui (δ)
uj(δ)
u∗i
u∗i , u∗ju∗j
Kalai-Smorodinsky deal
Negotiation
The Bargaining Problem
Strategic Solution Concepts
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
The Bargaining Problem
Strategic Solution Concepts
Strategic Solutions
Idea:
1 Formalize the bargaining process
2 Assume rational agents
3 Determine their equilibrium strategies for their bargainingprocess.
Negotiation
The Bargaining Problem
Strategic Solution Concepts
Rubinstein’s Alternating Offers
1 Two agents i and j
2 At each time step t one agent proposes a deal δ
3 The other can either accept or reject δ
4 Utilities decrease over time ui = λti ui (δ)
Negotiation
The Bargaining Problem
Strategic Solution Concepts
Theorem (Alternating Offers Bargaining Strategy)
The Rubinstein’s alternating offers game where the agents havecomplimentary linear utilities (ui (δ) = δ and uj(δ) = 1− ui (δ)) hasa unique subgame perfect equilibrium strategy where
agent i proposes a deal
δ∗i =1− λj
1− λiλj
and accepts the offer δj from j only if ui (δj) ≤ ui (δ∗j ),
agent j proposes a deal
δ∗j =1− λi
1− λiλj
and accepts the offer δi from i only if uj(δi ) ≤ uj(δ∗i ).
Negotiation
The Bargaining Problem
Strategic Solution Concepts
Alternating Offers Strategy
The theorem tells us that the best strategy for these agents ispropose a bid on the first time step which will be accepted by theother agent.
Negotiation
Monotonic Concession Protocol
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Monotonic Concession Protocol
monotonic-concession
1 δi ← arg maxδ ui (δ)2 Propose δi3 Receive δj proposal4 if ui (δj) ≥ ui (δi )5 then Accept δj6 else δi ← δ′i such that uj(δ
′i ) ≥ ε+ uj(δi ) and ui (δ
′i ) ≥ ui (δ
−)7 goto 2
Negotiation
Monotonic Concession Protocol
Monotonic Concession
δ
Utility
ui (δ)
uj(δ)
δ1i
ε δ2i
ε δ3i
ε
δ4i
δ1j
εδ2j
εδ3j
εδ4j
Negotiation
Monotonic Concession Protocol
Monotonic Concession Summary
Slow
Agents know others’ utility functions
Tricky last step: both might want other’s offer
Negotiation
Monotonic Concession Protocol
Zeuthen Strategy
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Monotonic Concession Protocol
Zeuthen Strategy
Zeuthen Strategy
1 Propose my best deal.
2 Let willingness to risk conflict for i be the utility i loses byaccepting j ’s offer divided by the utility i loses by notconceding and causing conflict. That is:
riski =ui (δi )− ui (δj)
ui (δi )
3 If riski < riskj then I must concede just enough so that in thenext round I do not have to concede again.
Negotiation
Monotonic Concession Protocol
Zeuthen Strategy
Zeuthen Strategy
zeuthen-monotonic-concession
1 δi ← arg maxδ ui (δ)2 Propose δi3 Receive δj proposal4 if ui (δj) ≥ ui (δi )5 then Accept δj
6 riski ←ui (δi )−ui (δj )
ui (δi )
7 riskj ←uj (δj )−uj (δi )
uj (δj )
8 if riski < riskj
9 then δi ← δ′i such that riski (δ′i ) > riskj
10 goto 211 goto 3
Negotiation
Monotonic Concession Protocol
Zeuthen Strategy
Zeuthen Strategy
Deals
ui (δ)
uj(δ)
δi = 0 δj = 6
ui (δ) = 5− δ,uj(δ) = 2
3δδ = {0 . . . 6}δi = 0, δj = 6
riski = 5−(−1)5 = 6
5 ,riskj = 4−0
4 = 1
Negotiation
Monotonic Concession Protocol
Zeuthen Strategy
Zeuthen Strategy
Deals
ui (δ)
uj(δ)
δi = 0
δj = 4.9
ui (δ) = 5− δ,uj(δ) = 2
3δδ = {0 . . . 6}δi = 0, δj = 6
riski = 5−(−1)5 = 6
5 ,riskj = 4−0
4 = 1 jmust concede, morethan 1.δj < 5
Negotiation
Monotonic Concession Protocol
Zeuthen Strategy
Zeuthen Characteristics
It is not guaranteed to maximize social welfare.
It is guaranteed to terminate, and any agreement it reacheswill be individually rational and Pareto optimal.
It is also in Nash equilibrium–if the other guy is using it thenyou have nothing to gain by not using it. Allows agents topublish their strategy.
But, sometimes risks are equal.
Requires agents to know eachother’s utility functions.
Negotiation
Monotonic Concession Protocol
One Step Protocol
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Monotonic Concession Protocol
One Step Protocol
One Step Protocol
one-step-negotiation
1 E ← {δ | ∀δ′ui (δ)uj(δ) ≥ ui (δ′)uj(δ
′)}2 δi ← arg maxδ∈E ui (δ)3 Propose δi4 Receive δj5 if ui (δj)uj(δj) < ui (δi )uj(δi )6 then Report error, j is not following strategy.7 Coordinate with j to choose randomly between δi and δj .
Negotiation
Monotonic Concession Protocol
One Step Protocol
One Step Protocol
Algorithm is in Nash equilibrium.
Negotiation
Negotiation as Distributed Search
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Negotiation as Distributed Search
Hill Climbing
ui (δ)
uj(δ)
δ0
Deals that Pareto dominate δ0
δ1
Negotiation
Ad-hoc Negotiation Strategies
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Ad-hoc Negotiation Strategies
Ad-hoc Negotiation Strategies
A linear discounts utility linearly.
A conceder concedes a lot initially.
An impatient demands a lot initially.
Negotiation
Task Allocation Problem
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Task Allocation Problem
Task Allocation Problem
The task allocation problem consists of:
T : tasksA: agentsci : s → < cost that i incurs in carrying out tasks s ⊆ T .δ represents allocation of tasks to agents.δ− is initial allocation
The cost function is monotonic.
The cost of doing nothing is 0.
Negotiation
Task Allocation Problem
Task Allocation Problem
δ si (δ) sj(δ) ci (δ) cj(δ) ui (δ) uj(δ)
δ1 ∅ {t1, t2, t3} 0 8 8 0δ2 {t1} {t2, t3} 1 4 7 4δ3 {t2} {t1, t3} 2 5 6 3δ4 {t3} {t1, t2} 4 7 4 1δ5 {t2, t3} {t1} 6 4 2 4δ6 {t1, t3} {t2} 5 3 3 5δ7 {t1, t2} {t3} 3 1 5 7δ8 {t1, t2, t3} ∅ 7 0 1 8
Negotiation
Task Allocation Problem
ui (δ)
uj(δ)
δ1
δ2
δ3
δ4
δ5
δ6
δ7
δ8
Negotiation
Task Allocation Problem
Payments
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Task Allocation Problem
Payments
Payments
1 Enable more deals by allowing payments.
2 This was the idea behind the original contract net protocol(Smith and Davis, 1981).
Negotiation
Task Allocation Problem
Payments
Payments
1 Enable more deals by allowing payments.
2 This was the idea behind the original contract net protocol(Smith and Davis, 1981).
Negotiation
Task Allocation Problem
Payments
Contract Net Protocol
manager
manager
contractor
contractor
contractor
Negotiation
Task Allocation Problem
Payments
Contract Net Protocol
manager
manager
contractor
contractor
contractor
task announcement
Eligibilityspecification.
Task abstraction.
Bid specification.
Expiration time.
Negotiation
Task Allocation Problem
Payments
Contract Net Protocol
manager
manager
contractor
contractor
contractor
bid
bid
Negotiation
Task Allocation Problem
Payments
Contract Net Protocol
manager
manager
contractor
contractor
contractor
award
Negotiation
Task Allocation Problem
Payments
Contract Net Protocol
manager
manager
contractor
contractor
contractor
contract
Negotiation
Task Allocation Problem
Payments
Payments Create Deals
ui (δ)
uj(δ)
δ0
δ1
New dominant deals
Negotiation
Task Allocation Problem
Payments
Payments Create Deals
ui (δ)
uj(δ)
δ0
δ1
New dominant deals
Negotiation
Task Allocation Problem
Payments
Additive Cost Functions
More formally,
Definition
A function c(s) is an additive cost function if for all s ⊆ T it istrue that
c(s) =∑t∈s
c(t).
They are easier to analyze.
Negotiation
Task Allocation Problem
Payments
Additive + Payments
Theorem
In a task allocation problem with an additive cost function wherewe only allow exchange of one task at a time, any protocol thatallows payments and always moves to dominant deals willeventually converge to the utilitarian solution .
Negotiation
Task Allocation Problem
Payments
ui (δ)
uj(δ)
δ1
δ2
δ3
δ4
δ5
δ6
δ7
δ8
Negotiation
Task Allocation Problem
Payments
Arbitrary Cost Functions
In general, not much we can say.
If any deal can be reached from any other deal (fullyconnected) then hill climbing will again reach the utilitariansolution.
Negotiation
Task Allocation Problem
Payments
Arbitrary Cost Functions
In general, not much we can say.
If any deal can be reached from any other deal (fullyconnected) then hill climbing will again reach the utilitariansolution.
Negotiation
Task Allocation Problem
Lying About Tasks
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Task Allocation Problem
Lying About Tasks
Lying About Tasks
Possible Lies
Not tell others about some tasks I have.
Make up tasks and hope I end up having to do them.
Make up tasks and create them if needed.
Assume known final deal. For example, Nash bargaining solution.
Negotiation
Task Allocation Problem
Lying About Tasks
Task Creation Example
δ si (δ) sj(δ) ui (δ) uj(δ)
δ1 ∅ {t1} 1 3δ2 {t1} ∅ 2 1
Create phony t2.
δ si (δ) sj(δ) ui (δ) uj(δ)
δ1 ∅ {t1, t2} 1 5δ2 {t1} {t2} 2 3δ3 {t2} {t1} 2 3δ4 {t1, t2} ∅ 8 1
Negotiation
Task Allocation Problem
Lying About Tasks
Task Creation Example
δ si (δ) sj(δ) ui (δ) uj(δ)
δ1 ∅ {t1} 1 3δ2 {t1} ∅ 2 1
Create phony t2.
δ si (δ) sj(δ) ui (δ) uj(δ)
δ1 ∅ {t1, t2} 1 5δ2 {t1} {t2} 2 3δ3 {t2} {t1} 2 3δ4 {t1, t2} ∅ 8 1
Negotiation
Task Allocation Problem
Lying About Tasks
Task Creation Example
δ si (δ) sj(δ) ui (δ) uj(δ)
δ1 ∅ {t1} 1 3δ2 {t1} ∅ 2 1
Create phony t2.
δ si (δ) sj(δ) ui (δ) uj(δ)
δ1 ∅ {t1, t2} 1 5δ2 {t1} {t2} 2 3δ3 {t2} {t1} 2 3δ4 {t1, t2} ∅ 8 1
Negotiation
Task Allocation Problem
Contracts
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Task Allocation Problem
Contracts
Contracts
Agents might want to de-commit on a contract.
Negotiation
Task Allocation Problem
Contracts
ui (δ)
uj(δ)
δ0
δ1 : i does task and j and pays nothing.
δ3 : i does nothing, j pays $2.
δ4 : i does task and j pays penalty of $1.
δ5 : i idle, pays $1 penalty, j pays $2.
δ2 : i does task and j and pays $2.
δ0: j does task and i is idle.
Negotiation
Task Allocation Problem
Contracts
ui (δ)
uj(δ)
δ0
δ1 : i does task and j and pays nothing.
δ3 : i does nothing, j pays $2.
δ4 : i does task and j pays penalty of $1.
δ5 : i idle, pays $1 penalty, j pays $2.
δ2 : i does task and j and pays $2.
δ0: j does task and i is idle.
Negotiation
Task Allocation Problem
Contracts
ui (δ)
uj(δ)
δ0
δ1 : i does task and j and pays nothing.
δ3 : i does nothing, j pays $2.
δ4 : i does task and j pays penalty of $1.
δ5 : i idle, pays $1 penalty, j pays $2.
δ2 : i does task and j and pays $2.
δ0: j does task and i is idle.
Negotiation
Task Allocation Problem
Contracts
ui (δ)
uj(δ)
δ0
δ1 : i does task and j and pays nothing.
δ3 : i does nothing, j pays $2.
δ4 : i does task and j pays penalty of $1.
δ5 : i idle, pays $1 penalty, j pays $2.
δ2 : i does task and j and pays $2.
δ0: j does task and i is idle.
Negotiation
Task Allocation Problem
Contracts
Contract Penalties
Penalties reduce risks.
But, if we can enforce penalties, why not just enforce originalcontracts?
Negotiation
Task Allocation Problem
Contracts
Contract Penalties
Penalties reduce risks.
But, if we can enforce penalties, why not just enforce originalcontracts?
Negotiation
Complex Deals
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Complex Deals
Complex Deals
A multi-dimensional deal is composed of a set of variablesx1, x2, . . . , xn with domains D1,D2, . . .Dn.
ui (δ)
Or, ui (δ) = c1u1i (x1) + c2u2
i (x2) + · · ·+ cnuni (xn)
Yes, this is a constraint optimization problem! But nowagents do not own the variables.
Negotiation
Complex Deals
Complex Deals
A multi-dimensional deal is composed of a set of variablesx1, x2, . . . , xn with domains D1,D2, . . .Dn.
ui (δ)
Or, ui (δ) = c1u1i (x1) + c2u2
i (x2) + · · ·+ cnuni (xn)
Yes, this is a constraint optimization problem! But nowagents do not own the variables.
Negotiation
Complex Deals
Convergence
δ
ui (δ)uj(δ)
δ1i
δ2i
δ1j
δ2j
δ3i ,j
Pareto domi-nate δ3
i ,j
Negotiation
Complex Deals
Annealing Over Complex Deals
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Complex Deals
Annealing Over Complex Deals
Negotiation with Mediator
annealing-mediator
1 Generate random deal δ.2 δaccepted ← δ
3 Present δ to agents.4 if both accept5 then δaccepted ← δ
6 δ ← mutate(δ)7 goto 38 if one or more reject9 then δ ← mutate(δaccepted)
10 goto 3
Negotiation
Complex Deals
Annealing Over Complex Deals
Hill Climbers and Annealers
Hill Climber Accepts a deal only if it has utility higher than itsreservation price ui (δ
−) and higher than that of thelast deal it accepted. That is, it monotonicallyincreases it reservation price as it accepts deals withhigher utility.
Annealer Use a simulated annealing algorithm. That is, theymaintain a temperature T and accept deals worsethan the last accepted deal with probability
max(1, e−∆UT ), where ∆U is the utility change
between the contracts.
Negotiation
Complex Deals
Annealing Over Complex Deals
Hill-Climbers and Annealers
Deals
Ui (δ) Uj(δ)
Negotiation
Complex Deals
Annealing Over Complex Deals
Hill-Climbers and Annealers
Deals
Ui (δ) Uj(δ)
δ1
Negotiation
Complex Deals
Annealing Over Complex Deals
Hill-Climbers and Annealers
Deals
Ui (δ) Uj(δ)
δ1
Hill Climber
Negotiation
Complex Deals
Annealing Over Complex Deals
Hill-Climbers and Annealers
Annealermax(1, e−
∆UT )
Deals
Ui (δ) Uj(δ)
δ1
Hill Climber
Negotiation
Complex Deals
Annealing Over Complex Deals
Hill-Climbers and Annealers
Annealermax(1, e−
∆UT )
Deals
Ui (δ) Uj(δ)
Hill Climber
δ2
Negotiation
Complex Deals
Annealing Over Complex Deals
Prisoner’s Dilemma, again!
Hill Climber Annealer
Hill Climber .73, .74 .99, .51
Annealer .51, .99 .84, .84
Negotiation
Complex Deals
Annealing Over Complex Deals
Adding Tit-for-Tat
Hill Climber Annealer T4T
Hill Climber 400, 400 700, 180 500, 340
Annealer 180, 700 550, 550 550, 550
T4T 340, 500 550, 550 550, 550
Negotiation
Argumentation-Based Negotiation
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Argumentation-Based Negotiation
Argument-Based Negotiations
Critique
Counter-proposal
Justify
Persuade
There are also threats, rewards, and appeals.
Negotiation
Argumentation-Based Negotiation
Argument-Based Negotiations
Critique the proposal.
A: I propose that you provide me with service Xunder conditions P.
B: I am happy with the price of X but the deliverydate is too late.
A: I propose that I will provide you with service Yif you provide me with X .
B: I don’t want Y .
Counter-proposal
Justify
Persuade
There are also threats, rewards, and appeals.
Negotiation
Argumentation-Based Negotiation
Argument-Based Negotiations
Critique
Counter-proposal
A: I propose that you provide me with service X .B: I propose that I provide you with service X if
you provide me with service Z .A: I propose that I provide you with service Y if
you provide me with service X .B: I propose that I provide you with service X if
you provide me with service Z .
Justify
Persuade
There are also threats, rewards, and appeals.
Negotiation
Argumentation-Based Negotiation
Argument-Based Negotiations
Critique
Counter-proposal
Justify his reason for adopting a particular negotiation stance.
A: I don’t have the software for delivering service X .
Persuade
There are also threats, rewards, and appeals.
Negotiation
Argumentation-Based Negotiation
Argument-Based Negotiations
Critique
Counter-proposal
Justify
Persuade the other agent to change its negotiation stance.
A: Service X is much better than you think, look atthis report.
There are also threats, rewards, and appeals.
Negotiation
Argumentation-Based Negotiation
Argument-Based Negotiations
Critique
Counter-proposal
Justify
Persuade
There are also threats, rewards, and appeals.
These techniques help
build model of opponent’s utility function,
eliminate whole sets of deals,
change the other agent’s utility function,
change my utility function.
Negotiation
Negotiation Networks
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Negotiation Networks
Negotiation Networks
Definition
A negotiation network problem involves a set of agents A and setof sets of deals. Each set of deals ∆i involves only a subset ofagents ∆a
i ⊆ A and always includes the no-deal deal δ−. A solution~δ to the problem is a set of deals, one from each ∆i set, such thatall the deals that each agent is involved in are compatible witheach other. We thus define
ci (δ, δ′) =
{1 if δ and δ′ are compatible0 otherwise
Negotiation
Negotiation Networks
Negotiation Network
j
i
k
∆1 ∆2
∆3
Negotiation
Negotiation Networks
Network Exchange Theory
1 Introduction
2 The Bargaining ProblemAxiomatic Solution ConceptsStrategic Solution Concepts
3 Monotonic Concession ProtocolZeuthen StrategyOne Step Protocol
4 Negotiation as Distributed Search
5 Ad-hoc Negotiation Strategies
6 Task Allocation ProblemPaymentsLying About TasksContracts
7 Complex DealsAnnealing Over Complex Deals
8 Argumentation-Based Negotiation
9 Negotiation NetworksNetwork Exchange Theory
Negotiation
Negotiation Networks
Network Exchange Theory
Network Exchange Theory
i j
−10−1
1 −1
The coercion network.
Negotiation
Negotiation Networks
Network Exchange Theory
Equi-Resistance
i j10
Negotiation
Negotiation Networks
Network Exchange Theory
Equi-Resistance
i j10
i ’s resistance to payment p is given by
ri =pmaxi − pi
pi − pconi
wherepmaxi = Maximum i could get, 10
andpconi = Conflict deal, 0
Negotiation
Negotiation Networks
Network Exchange Theory
Equi-Resistance
i j10
NET tells us that exchange happens at equi-resistance:
ri =pmaxi − pi
pi − pconi
=pmaxj − pj
pj − pconj
= rj .
We can represent this graphically by simply replacing pj with10− pi in j ’s resistance equation rj and plotting the two curves riand rj . The point at which the curves cross is the point ofexchange.
Negotiation
Negotiation Networks
Network Exchange Theory
Equi-Resistance
i j10
p
ri (p) rj(p)
Negotiation
Negotiation Networks
Network Exchange Theory
Iterated Equi-Resistance
i j k10 10
Negotiation
Negotiation Networks
Network Exchange Theory
Iterated Equi-Resistance
i j k10 10
1 Apply Equi-resistance to i j10
.
2 Apply Equi-resistance to j k10
.
3 Repeat until quiescence.
Negotiation
Negotiation Networks
Network Exchange Theory
Iterated Equi-Resistance
i j k10 10
1 Apply Equi-resistance to i j10
. Gives us pj = 5.
2 Apply Equi-resistance to j k10
.
3 Repeat until quiescence.
Negotiation
Negotiation Networks
Network Exchange Theory
Iterated Equi-Resistance
i j k10 10
1 Apply Equi-resistance to i j10
. Gives us pj = 5.
2 Apply Equi-resistance to j k10
. Let pconj = 5 and apply
equi-resistance again.
3 Repeat until quiescence.
Negotiation
Negotiation Networks
Network Exchange Theory
NET Limitations
Only tested on small networks.
Multiple equilibriums.
Might never settle down.
Still, viable descriptive solution.