Multi-Agent Systems Negotiation

1. Multi-Agent SystemsNegotiation Shari Naik

2. Negotiation • Inter-agent cooperation • Conflict resolution • Agents communicate respective desires • Compromise to mutually beneficial agreement

3. Negotiation in Cooperative domains • Jefferey Rosenschein • Gilad Zlatkin

4. Domains • Distributed problem solving • Distributed but centrally designed AI systems • Global problem to solve • Multiagent systems • Distributed, with different designers • Agents working for different goals • Task Oriented • State Oriented • Worth Oriented

5. Task Oriented Domain • Non-conflicting jobs • Negotiation : Redistribute tasks to everyone’s mutual benefit • Example - Postmen domain

6. State Oriented Domain • Goals are acceptable final states • Have side effects - agent doing one action might hinder or help another agent • Negotiation : develop joint plans and schedules for the agents, to help and not hinder other agents • Example – Slotted blocks world

7. Rates the acceptability of final states Negotiation : a joint plan, schedules, and goal relaxation. May reach a state that might be a little worse that the ultimate objective Example – Multi-agent Tile world Worth Oriented Domain

8. Task Oriented Domain • Tuple <T, A, c> • T - set of tasks, • A – List of agents • C - cost function from any set of tasks to a real number • Encounter(goal) - a list, T1, … Tn, of finite sets of tasks from the task set T, such that each agent needs to achieve all the tasks in its set.

9. Building blocks • Precise specification of the domain • Negotiation protocol • Negotiation strategy • Assumptions • Expected Utility Maximizer • Complete Knowledge • No History • Commitments are Verifiable

10. Domain Definitions • Graph (City Map) G = G(V,E) • v eV => nodes (address / Post office) • e e E => edges (roads) • Weight function (Distance of road) • W : EIN • Letters for agent A : LA • "Agent Li : I e {A,B} • Letters (LA W LB) = f • Cost(L) e IN => weight of minimum weight cycle that starts at PO and visits all vertices of L and ends at PO

11. Definitions • Deal – Division of LAULB to two disjoint subsets, (DA,DB) such that • DAUDB= LAULB • DAWDB=f • Utility – Difference between the cost of achieving his goal alone and the cost of his part of the deal • Utilityi(DA,DB) = Cost(Li) – Cost(Di)

12. Properties of a Deal (d) • Individual rational • "{A,B}, Utilityi(d) >= 0 • Pareto optimal – there does not exist another deal d1 such that d1 > d • Negotiation set – set of deals that are individual rational and pareto optimal • P(d) – Product of the two agent utilities from d

13. Negotiation Protocol • A product maximizing ngotiation protocol • One step protocol • Concession protocol • At t >= 0, A offers d(A,t) and B offers d(B,t), such that • Both deals are from the negotiation set • "i e {A,B} and "t >0, Utilityi(d(i,t)) <= Utilityi(d(i,t-1)) • Negotiation ending • Conflict - Utilityi(d(i,t)) = Utilityi(d(i,t-1)) • Agreement, $j !=i e {A,B},Utilityj(d(i,t)) >= Utilityj(d(j,t)) • Only A => agree d(B,t) • Only B => agree d(A,t) • Both A,B => agree d(k,t) such that P(d(k))=max{P(d(A)),P(d(B))} • Both A,B and P(d(A))=P(d(B)) => flip a coin Pure deals Mixed deal

14. Negotiation Strategies • How an agent should act given a set of rules. • Definition – Function from the history of the negotiation to the current message • Risk - an indication of how much an agent is willing to risk a conflict by sticking to its last offer • Risk(A,t) = Utility, A loses accepting B’s offer Utility, A loses by causing a conflict • Risk  Loss • Rational Negotiation Stratergy – At any step t+1, A sticks to his last offer if, Risk(A,t) > Risk(B,t)

15. Negotiation Strategies Cont • Zeuthen Strategy – • Start – A offers B the minimal offer • UtilityB(d(A,1)) = mindeNS{UtilityB(d) } • Next - A will make a minimal sufficient concession at step t+1 iff Risk(A,t)<=Risk(B,t) • If both agents follow the above stratergy, they will agree on a deal d* e NS, such that P(d*)=maxdeNS {P(d)}

16. Equilibrium • A negotiation strategy s will be in equilibrium if under the assumption that A uses s, B prefers s to any other strategy • Zeuthen strategy is not in equilibrium

17. Mixed deal • Element of probability – Agents will perform (DA,DB) with probability p or (DA,DB) with probability 1-p • Costi([(DA,DB):p]) = pCost(Di) + (1-p)Cost(Dj) • Utilityi([d:p]) = Cost(Li) – Costi([d:p]) • All or nothing deal – 0<=p<=1 such that • mixed deal m = [({LA,LB}, f ):p] e NS • P(m) = maxdeNSp(d)

18. Incomplete Information • G and w – common knowledge • i knows Li, not Lj : j!=I • Solution • Exchange missing information • Penalty for lie • Possible lies • False information • Hiding letters • Phantom letters • Not carry out a commitment

19. Hidden letters • Utility of A • Expected(on telling the truth) = 4 • Pure deal – [(d,f):1/2] = 6 • Mixed deal - [(d,f):3/8] = 33/4

20. Phantom letters • Utility of A • Expected(on telling the truth) = 3 • Pure deal – [(d,f):1/2] = 4 • Mixed deal – possibility of being caught (all or nothing deal)

21. Subadditive Task Oriented Domain • the cost of the union of tasks is less than or equal to the sum of the costs of the separate sets • for finite X,Y in T, c(X U Y) <= c(X) + c(Y)). • Example of non additive TOD

22. Incentive compatible Mechanism • L lying is beneficial • T  Honesty is better • T/P  Lying can be beneficial, but chances of being caught

23. Concave Task Oriented Domain • We have 2 tasks X and Y, where X is a subset of Y • Another set of task Z is introduced • c(X U Z) - c(X) >= c(Y U Z) - c(Y).

24. Modular TOD • c(X U Y) = c(X) + c(Y) 2 c(X WY).

25. Multi Agent Compromise via Negotiation • Katia Sycara

26. Negotiation process for conflicting goals • Identify potential interactions • Modify intentions to avoid harmful interactions or create cooperative situations • Techniques required • Representing and maintaining belief models • Reasoning about other agents beliefs • Influencing other agents intentions and beliefs

27. PERSUADER • Program to resolve problems in labor relations domain • Agents • Company • Union • Mediator • Tasks • Generation of proposal • Generation of counter proposal based on feedback from dissenting party • Persuasive argumentation

28. Negotiation Methods • Case based Reasoning • Preference analysis

29. Case Based Reasoning • Uses past negotiation experiences as guides to present negotiation • Process • Retrieve appropriate precedent cases from memory • Select the most appropriate case • Construct and appropriate solution • Evaluate solution for applicability to current case • Modify the solution appropriately

30. Case Based Reasoning • Cases organized and retrieved according to conceptual similarities. • Advantages • Minimizes need for information exchange • Avoids problems by reasoning from past failures. Intentional reminding. • Repair for past failure is used. Reduces computation.

31. Preference Analysis • From scratch planning method • Based on multi attribute utility theory • Gets a overall utility curve out of individual ones. • Expresses the tradeoffs an agent is willing to make. • Property of the proposed compromise • Maximizes joint payoff • Minimizes payoff difference

32. Persuasive argumentation • Argumentation goals • Ways that an agents beliefs and behaviors can be affected by an argument • Increasing payoff • Change importance attached to an issue • Changing utility value of an issue

33. Narrowing differences • Gets feed back from rejecting party • Objectionable issues • Reason for rejection • Importance attached to issues • Increases payoff of rejecting party by greater amount than reducing payoff for agreed parties.

34. Experiments • Without Memory – 30% more proposals • Without argumentation – lesser proposals and better solutions • No failure avoidance – more proposals with objections • No preference analysis – Oscillatory condition • No feedback – communication overhead by 23%

35. Thank You