Negotiation Monotonic Concession Protocol Zeuthen Strategy 1 Introduction The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network 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 by accepting j ’s offer divided by the utility i loses by not conceding and causing conflict. That is: risk i = u i ( δ i ) − u i ( δ j ) u i ( δ i ) 3 If risk i < risk j then I must concede just enough so that in the next round I do not have to concede again.
Negotiation Monotonic Concession Protocol Zeuthen Strategy Zeuthen Strategy zeuthen-monotonic-concession 1 δ i ← arg max δ u i ( δ ) 2 Propose δ i 3 Receive δ j proposal 4 if u i ( δ j ) ≥ u i ( δ i ) 5 then Accept δ j risk i ← u i ( δ i ) − u i ( δ j ) 6 u i ( δ i ) risk j ← u j ( δ j ) − u j ( δ i ) 7 u j ( δ j ) 8 if risk i < risk j then δ i ← δ ′ i such that risk i ( δ ′ 9 i ) > risk j 10 goto 2 11 goto 3
Negotiation Monotonic Concession Protocol Zeuthen Strategy Zeuthen Strategy u i ( δ ) u j ( δ ) u i ( δ ) = 5 − δ , u j ( δ ) = 2 3 δ δ = { 0 . . . 6 } δ i = 0 , δ j = 6 risk i = 5 − ( − 1) = 6 5 , 5 risk j = 4 − 0 = 1 4 δ i = 0 δ j = 6 Deals
Negotiation Monotonic Concession Protocol Zeuthen Strategy Zeuthen Strategy u i ( δ ) u i ( δ ) = 5 − δ , u j ( δ ) = 2 u j ( δ ) 3 δ δ = { 0 . . . 6 } δ i = 0 , δ j = 6 risk i = 5 − ( − 1) = 6 5 , 5 risk j = 4 − 0 = 1 j 4 must concede, more than 1. δ j < 5 δ j = 4 . 9 δ i = 0 Deals
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 reaches will be individually rational and Pareto optimal. It is also in Nash equilibrium–if the other guy is using it then you have nothing to gain by not using it. Allows agents to publish their strategy. But, sometimes risks are equal. Requires agents to know eachother’s utility functions.
Negotiation Monotonic Concession Protocol One Step Protocol 1 Introduction The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network Exchange Theory
Negotiation Monotonic Concession Protocol One Step Protocol One Step Protocol one-step-negotiation 1 E ← { δ | ∀ δ ′ u i ( δ ) u j ( δ ) ≥ u i ( δ ′ ) u j ( δ ′ ) } 2 δ i ← arg max δ ∈ E u i ( δ ) 3 Propose δ i 4 Receive δ j 5 if u i ( δ j ) u j ( δ j ) < u i ( δ i ) u j ( δ i ) 6 then Report error, j is not following strategy. 7 Coordinate with j to choose randomly between δ i and δ j .
Negotiation Monotonic Concession Protocol One Step Protocol One Step Protocol Algorithm is in Nash equilibrium.
Negotiation Negotiation as Distributed Search 1 Introduction The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network Exchange Theory
Negotiation Negotiation as Distributed Search Hill Climbing Deals that Pareto dominate δ 0 u j ( δ ) δ 1 δ 0 u i ( δ )
Negotiation Ad-hoc Negotiation Strategies 1 Introduction The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network 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 The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network Exchange Theory
Negotiation Task Allocation Problem Task Allocation Problem The task allocation problem consists of: T : tasks A : agents c i : s → ℜ 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 s i ( δ ) s j ( δ ) c i ( δ ) c j ( δ ) u i ( δ ) u j ( δ ) δ δ 1 ∅ { t 1 , t 2 , t 3 } 0 8 8 0 δ 2 { t 1 } { t 2 , t 3 } 1 4 7 4 δ 3 { t 2 } { t 1 , t 3 } 2 5 6 3 δ 4 { t 3 } { t 1 , t 2 } 4 7 4 1 δ 5 { t 2 , t 3 } { t 1 } 6 4 2 4 δ 6 { t 1 , t 3 } { t 2 } 5 3 3 5 δ 7 { t 1 , t 2 } { t 3 } 3 1 5 7 δ 8 { t 1 , t 2 , t 3 } ∅ 7 0 1 8
Negotiation Task Allocation Problem δ 8 δ 7 δ 6 δ 5 δ 2 u j ( δ ) δ 3 δ 4 δ 1 u i ( δ )
Negotiation Task Allocation Problem Payments 1 Introduction The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network Exchange Theory
Negotiation Task Allocation Problem Payments Payments 1 Enable more deals by allowing payments.
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 contractor manager contractor contractor manager
Negotiation Task Allocation Problem Payments Contract Net Protocol task announcement contractor manager contractor Eligibility specification. contractor manager Task abstraction. Bid specification. Expiration time.
Negotiation Task Allocation Problem Payments Contract Net Protocol contractor d b i manager contractor bid contractor manager
Negotiation Task Allocation Problem Payments Contract Net Protocol contractor award manager contractor contractor manager
Negotiation Task Allocation Problem Payments Contract Net Protocol contractor contract manager contractor contractor manager
Negotiation Task Allocation Problem Payments Payments Create Deals u j ( δ ) δ 1 δ 0 u i ( δ )
Negotiation Task Allocation Problem Payments Payments Create Deals New dominant deals u j ( δ ) δ 1 δ 0 u i ( δ )
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 is true that � c ( s ) = c ( t ) . t ∈ s They are easier to analyze.
Negotiation Task Allocation Problem Payments Additive + Payments Theorem In a task allocation problem with an additive cost function where we only allow exchange of one task at a time, any protocol that allows payments and always moves to dominant deals will eventually converge to the utilitarian solution .
Negotiation Task Allocation Problem Payments δ 8 δ 7 δ 6 δ 5 δ 2 u j ( δ ) δ 3 δ 4 δ 1 u i ( δ )
Negotiation Task Allocation Problem Payments Arbitrary Cost Functions In general, not much we can say.
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 (fully connected) then hill climbing will again reach the utilitarian solution.
Negotiation Task Allocation Problem Lying About Tasks 1 Introduction The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network 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 s i ( δ ) s j ( δ ) u i ( δ ) u j ( δ ) δ 1 ∅ { t 1 } 1 3 δ 2 { t 1 } ∅ 2 1
Negotiation Task Allocation Problem Lying About Tasks Task Creation Example δ s i ( δ ) s j ( δ ) u i ( δ ) u j ( δ ) δ 1 ∅ { t 1 } 1 3 δ 2 { t 1 } ∅ 2 1 Create phony t 2 .
Negotiation Task Allocation Problem Lying About Tasks Task Creation Example δ s i ( δ ) s j ( δ ) u i ( δ ) u j ( δ ) δ 1 ∅ { t 1 } 1 3 δ 2 { t 1 } ∅ 2 1 Create phony t 2 . δ s i ( δ ) s j ( δ ) u i ( δ ) u j ( δ ) δ 1 ∅ { t 1 , t 2 } 1 5 δ 2 { t 1 } { t 2 } 2 3 δ 3 { t 2 } { t 1 } 2 3 δ 4 { t 1 , t 2 } ∅ 8 1
Negotiation Task Allocation Problem Contracts 1 Introduction The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network Exchange Theory
Negotiation Task Allocation Problem Contracts Contracts Agents might want to de-commit on a contract.
Negotiation Task Allocation Problem Contracts u j ( δ ) δ 0 u i ( δ ) δ 0 : j does task and i is idle.
Negotiation Task Allocation Problem Contracts δ 2 : i does task and j and pays $2. u j ( δ ) δ 0 u i ( δ ) δ 0 : j does task and i is idle.
Negotiation Task Allocation Problem Contracts δ 1 : i does task and j and pays nothing. δ 2 : i does task and j and pays $2. u j ( δ ) δ 3 : i does nothing, j pays $2. δ 0 u i ( δ ) δ 0 : j does task and i is idle.
Negotiation Task Allocation Problem Contracts δ 1 : i does task and j and pays nothing. δ 4 : i does task and j pays penalty of $1. δ 2 : i does task and j and pays $2. u j ( δ ) δ 5 : i idle, pays $1 penalty, j pays $2. δ 3 : i does nothing, j pays $2. δ 0 u i ( δ ) δ 0 : j does task and i is idle.
Negotiation Task Allocation Problem Contracts Contract Penalties Penalties reduce risks.
Negotiation Task Allocation Problem Contracts Contract Penalties Penalties reduce risks. But, if we can enforce penalties, why not just enforce original contracts?
Negotiation Complex Deals 1 Introduction The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network Exchange Theory
Negotiation Complex Deals Complex Deals A multi-dimensional deal is composed of a set of variables x 1 , x 2 , . . . , x n with domains D 1 , D 2 , . . . D n . u i ( δ ) Or, u i ( δ ) = c 1 u 1 i ( x 1 ) + c 2 u 2 i ( x 2 ) + · · · + c n u n i ( x n )
Negotiation Complex Deals Complex Deals A multi-dimensional deal is composed of a set of variables x 1 , x 2 , . . . , x n with domains D 1 , D 2 , . . . D n . u i ( δ ) Or, u i ( δ ) = c 1 u 1 i ( x 1 ) + c 2 u 2 i ( x 2 ) + · · · + c n u n i ( x n ) Yes, this is a constraint optimization problem! But now agents do not own the variables.
Negotiation Complex Deals Convergence δ 1 u i ( δ ) j u j ( δ ) δ 2 j Pareto domi- δ 3 i , j nate δ 3 i , j δ 2 i δ 1 i δ
Negotiation Complex Deals Annealing Over Complex Deals 1 Introduction The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network Exchange Theory
Negotiation Complex Deals Annealing Over Complex Deals Negotiation with Mediator annealing-mediator 1 Generate random deal δ . δ accepted ← δ 2 3 Present δ to agents. 4 if both accept 5 then δ accepted ← δ 6 δ ← mutate( δ ) 7 goto 3 8 if one or more reject 9 then δ ← mutate( δ accepted) 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 its reservation price u i ( δ − ) and higher than that of the last deal it accepted. That is, it monotonically increases it reservation price as it accepts deals with higher utility. Annealer Use a simulated annealing algorithm. That is, they maintain a temperature T and accept deals worse than the last accepted deal with probability max(1 , e − ∆ U T ), where ∆ U is the utility change between the contracts.
Negotiation Complex Deals Annealing Over Complex Deals Hill-Climbers and Annealers U i ( δ ) U j ( δ ) Deals
Negotiation Complex Deals Annealing Over Complex Deals Hill-Climbers and Annealers U i ( δ ) U j ( δ ) δ 1 Deals
Negotiation Complex Deals Annealing Over Complex Deals Hill-Climbers and Annealers U i ( δ ) U j ( δ ) Hill Climber δ 1 Deals
Negotiation Complex Deals Annealing Over Complex Deals Hill-Climbers and Annealers U i ( δ ) U j ( δ ) Hill Climber Annealer max(1 , e − ∆ U T ) δ 1 Deals
Negotiation Complex Deals Annealing Over Complex Deals Hill-Climbers and Annealers U i ( δ ) U j ( δ ) Hill Climber Annealer max(1 , e − ∆ U T ) δ 2 Deals
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 The Bargaining Problem 2 Axiomatic Solution Concepts Strategic Solution Concepts Monotonic Concession Protocol 3 Zeuthen Strategy One Step Protocol 4 Negotiation as Distributed Search Ad-hoc Negotiation Strategies 5 Task Allocation Problem 6 Payments Lying About Tasks Contracts 7 Complex Deals Annealing Over Complex Deals Argumentation-Based Negotiation 8 Negotiation Networks 9 Network 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 X under conditions P . B: I am happy with the price of X but the delivery date is too late. A: I propose that I will provide you with service Y if 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 at this 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.
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