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- 1. AgentSchool 2013 at Dunedin, New Zealand. (Dec. 1, 2013) Automated Negotiation Takayuki Ito Dept. of Computer Science / School of Techno-Business Administration Nagoya Institute of Technology, Japan ito@nitech.ac.jp
- 2. Takayuki Ito Associate Professor, Nagoya Institute of Technology E-mail : ito@nitech.ac.jp http:/ /www.itolab.nitech.ac.jp/~ito/ 2000 Dr. of Engineering, Nagoya Institute of Technology 1999 Research fellow, Japan Society for the Promotion of Science (JSPS). 2000 Visiting Researcher, USC/ISI. 2001 Assoc. Professor, Japan Advanced Insti. of Sci. & Tech. (JAIST). 2003 Assoc. Professor, Dept. of CSE, Nagoya Institute of Technology. 2005 Visiting Scholar, Computer Science, Harvard University. 2005 Visiting Researcher, MIT Sloan School of Management. 2006-Now Assoc. Prof., School of Techno-Business Admin., Nagoya Institute of Technology. 2008 Visiting Scientist, Center for Collective Intelligence, MIT Sloan School of Management. 2010 JST PREST researcher (super challenging type) 2011 Japanese Cabinet Office’ NEXT fund Principal Investigator s 2013 AAMAS 2013 Program Chair
- 3. Area : Computer Science, Artiﬁcial Intelligence, Multi-Agent Systems, Automated Negotiations, Auction Theory, Mechanism Design, Smart City, Smart Grid, etc. Main achievements: •2013 JSPS Award •Prizes for Science and Technology, The Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology, 2013. •The NEXT Funding Program from the Japanese Cabinet Ofﬁce •The Young Scientists' Prize, The Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology, 2007. •Nagao Special Researcher Award, IPSJ 2007 •Best Paper Award, The Fifth International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS2006, 1/553), 2006. •2005 Best Paper Award, Japan Society for Softoware Science and Technoglogy. •2004 IPA Exploratory Software Creation Project, Super Creator Award.
- 4. Today’s schedule • Part 1: Introduction to Automated Negotiation • Part 2: Bargaining : Game Theoretic Approaches • Part 3: Multi-issue Negotiation : Heuristic Approaches • Part 4: Automated Negotiating Agent Competition
- 5. Part 1 Introduction to Negotiation
- 6. What is Negotiation? • Negotiation is a form of interaction in which a group of agents with conﬂicting interests try to come to a mutually acceptable agreement over some outcome. • The outcome is typically represented in terms of the allocation of resources (commodities, services, time, money, CPU cycles, etc.) • Agents’ interests are conﬂicting in the sense that they cannot be simultaneously satisﬁed, either partially or fully (= trade-off) • Automated negotiation would be negotiation that is automated with some computation support, e.g., fully automated negotiation among computational agents, partially automated negotiation with a computational mediator with human negotiators, etc.
- 7. What is Negotiation? “Negotiation can be seem as a distributed search through a space of potential agreements.” [Jennings 2001] [Jennings 2001] N. R. Jennings, P. Faratin, A. R. Lomuscio, S. Parsons, C. Sierra and M. Wooldridge, Automated Negotiation: Prospects, Methods and Challenges, International Journal of Group Decision and Negotiation, 10(2):199-215, 2001
- 8. What is Negotiation? issue (attribute) 2 “Negotiation can be seem as a distributed search through a space of potential agreements.” [Jennings 2001] issue (attribute) 1 This negotiation space can be seen as 2 dimensional [Jennings 2001] N. R. Jennings, P. Faratin, A. R. Lomuscio, S. Parsons, C. Sierra and M. Wooldridge, Automated Negotiation: Prospects, Methods and Challenges, International Journal of Group Decision and Negotiation, 10(2):199-215, 2001
- 9. bilateral negotiation • We focus on “bilateral negotiations” , that is, negotiations involving two agents • Multi-party negotiations refers negotiations involving many of ag ents. In g en e ral, auctio ns an d m e chan isms can been seen as mu lti-party negotiations. Also, some researchers now focusing on heuristic-based one.
- 10. Main ingredients of Negotiation 1. The negotiation object, which deﬁnes the set of possible outcomes 2. The agents conducting the negotiation 3. The protocol according to which agents search for a speciﬁc agreement 4. The individual strategies that determine the agents’ behavior based on their preferences over the outcomes
- 11. Negotiation outcomes • There are many ways to deﬁne the outcomes. • Also called as agreements or deals. • Characteristics • Continuous or discrete • Single issue or multiple issues
- 12. Example 1 • 1.0 litter milk between Alice and Bob • The issue is (dividing) milk, that is single issue & continuous • The possible outcome can be represented as a number in interval [0,1.0]. • One possible outcome is 0.2l for Alice and 0.8l for Bob.
- 13. Example 2 • Parking slot 1 and 2 for Charles and Daniel • The issue is 3 parking slots, that is single issue & discrete • The possible outcome can be represented as assignment of the parking slot • One possible outcome is slot 1 for Charles and slot 2 for Bob
- 14. Example 3 • Buying a house between Seller and Buyer • The issues are price, design, and place (3 issues), that is multiple issue (& discrete and continuous) • The possible outcome can be represented as a tuple of values of the issues. • One possible outcome is ($150,000, modern, Dunedin)
- 15. Preferences • Two different agents prefer different allocations of the resources. • Preference representation or “ordinal utility” • Binary preference relation : • means outcome o1 is at least as good as outcome o2 for agent i • means and it is not a case that
- 16. Utility function • One way to deﬁne preference relation for agent i is to deﬁne a utility function to assign real number to each possible outcome (cardinal utility <-> ordinal utility). • The utility function have if • In multi-issue negotiation, it is possible to have a multiattribute utility function which maps a vector of attribute values to a real number. • A rational agent attempts to reach a deal that maximizes his/her utility. represents the relation . when we
- 17. Example • There are many deﬁnitions of utility functions • Example: • A quasi-linear utility function • The utility, ui, for an item, x, is deﬁned as, vi, the value of it minus the cost, ci, to acquire it. • ui(x) = vi(x) - ci(x)
- 18. Protocols • Given a set of the agents and their preferences/ utilities, we need a protocol. • A protocol is rules of interaction for enabling the agents to search for an agreement • One-shot or repeated • There are many protocols proposed so far. • Example: Alternative-offer protocol (we will see this in the later section), auction, mediator, etc.
- 19. Strategy • Given a set of agents, their preferences, and an agreed protocol, the ﬁnal ingredient is the agent’s strategy • The strategy may specify what offer to make next or what information to reveal (truthfully or not). • A rational agent’s strategy must aim to achieve the best possible outcome for him/her. • Game-theory is analyzing agents’ strategic behavior.
- 20. Pareto Optimality • At the Pareto optimal situation, without reducing another agent’s utility, there is no agent who can increase his/her utility. • An outcome d is Pareto efﬁcient (Pareto optimal) if there is no outcome that is better for at least one agent and not worse for the other agent • There is no game outcome d’ for agents A and B s.t. [ uA(d’) ≥ uA(d) and uB(d’) ≥ uB(d) ] and [ uA(d’) > uA(d) or uB(d’) > uB(d) ]
- 21. Example: Cake division • When dividing one cake, it is Pareto optimal if the entire cake is completely divided and allocated to members, and there is no remaining pieces • Pareto optimal does not mean fairness Blue or yellow can increase his/ her cake without reducing opponent’s cake! Without reducing opponent’s utility, there is no agent who can increase his/her cake.
- 22. Approaches • • • Bargaining: Game Theoretic Approaches : Part 2 • How game theory can be used to analyze negotiation. • Cooperative game or non-cooperative game • Assumptions: • Rules of the game, preferences & beliefs of all players are common knowledge • A2: Full rationality on the part of all players (=unlimited computation) • Preferences encoded in a (limited) set of player types (utility functions) • Closed systems, predetermined interaction, small sized games Heuristic Approaches (AI approach): Part 3 • No common knowledge or perfect rationality assumptions needed • Agent behaviour is modeled directly • Suitable for open, dynamic environments • Space of possibilities is very large Argumentation Approaches : out of scope in this lecture • Based on formal logics of dialogue games
- 23. Cooperative game or Noncooperative game • There are two ways to model bilateral negotiations : using cooperative game or using non-cooperative game • • • In cooperative games, agreements are enforceable or binding, and it’s possible for the agents to negotiate outcomes that are mutually beneﬁcial. In non-cooperative game, the agents are self-interested and thus they have incentive to deviate from an agreement to improve his/her utility Thus, a same game would have the different outcome between cooperative games and non-cooperative games
- 24. Prisoner’s Dilemma: In non-cooperative game Bob Silent Alex Confess Silent 8,8 0 , 10 Confess 10 , 0 5,5
- 25. Prisoner’s Dilemma: In cooperative game Bob Silent Alex Confess Silent 8,8 0 , 10 Confess 10 , 0 5,5
- 26. Cooperative game based bargaining • Most of work on cooperative models of bargaining followed from the seminal work of Nash [Nash1950, Nash1953] • [Nash1950] J.F. Nash, The bargaining problem, Econometrica, 18:155-162, 1950 • [Nash1953] J.F. Nash, Two-person cooperative game, Econometrica, 21:128-140, 1953 • Nash analyzed the bargaining problem and deﬁned a solution/outcome for it using an axiomatic approach • Nash deﬁned a solution without the details of negotiation process • The solution is called as “Nash solution” for bargaining/negotiation problems and it is widely used as one of the ideal solutions. • Assumption • The two agents are perfectly rational: each can accurately compare its preferences for the possible outcomes, they are equal in bargaining skill, and each has complete knowledge of the preference of the other.
- 27. Nash solution • Deﬁnition: A bargaining problem is deﬁned as a pair (S, d). A bargaining solution is a function f that maps every barging problem (S, d) to an outcome in S, i.e., f(S,d)-> S • S is bargaining set that is the set of all utility pairs result from an agreement. • d is the disagreement point where each agent i gets ui(d) even if there is no agreement • Deﬁnition : Nash solution is deﬁned as follows: ! • Nash product : (u1(x)-u1(d)) x (u2(x)-u2(d))
- 28. u1(x1) u1(d1) 0 (s1,d2) (d1,d2) u2(d2) S: feasible set (d1,s2) u2(x2)
- 29. u1(x1) (s1,d2) (u1(x)-u1(d))x(u2(x)-u2(d)) Nash solution u1(d1) 0 (d1,d2) u2(d2) S: feasible set (d1,s2) u2(x2)
- 30. Nash solution • Nash proved that the solution that satisﬁes the ﬁve axioms below is Nash solution and its unique. • Axiom 1 (Individual Rationality) : Each agent can get at least disagreement point. f(S,d) >= d. • Axiom 2 (Symmetry) : The solution is independent form agent’s name, like A or B. • Axiom 3 (Pareto Optimality) • Axiom 4 (Invariance from Aﬁne Transformation) : The solution should not change as a result of linear changes to the utility for either agent • Axiom 5 (Independence of Irrelevant Alternatives) : Eliminating feasible alternatives that are not chosen should not affect the solution. Namely,
- 31. Bargaining based on non-cooperative game • Usually, non-cooperative model of bargaining speciﬁes a procedure of negotiation. • Most inﬂuential non-cooperative model is the wallowing Rubinstein’s work. [Rubinstein 1982] Perfect equilibrium in a bargaining model. Econometrica, 50(1):97-109, Jan 1982. [Rubinstein 1985] A bargaining model with incomplete information about time preference. Econometrica, 53:1151-1172, Jan 1985.
- 32. A brief overview of Rubinstein’s bargaining [Rubinstein 1982] Perfect equilibrium in a bargaining model. Econometrica, 50(1):97-109, Jan 1982. • There are two agents (players) and a unit of good, a pie, to be split between them (Issue is divisible). • If agent a gets a share of gets . • If agents cannot reach an agreement, they do not get anything. then agent b
- 33. Alternating offers protocol θ • This game is played over a series of discrete time periods t = 1,2,3,... • The agents take turns in making offers. • t = 1, player A proposes an offer (Xa,t=1). If player B accepts A’s offer, they reach an agreement. If not (reject), goto t = 2. θ s(θ) • • t = 2, player B proposes a counter offer (Xb,t=2). If player A accepts B’s offer, they reach an agreement. If not (reject), goto t = 3. t = 3, ... θ s(θ) M θ s(θ) M’ Concretely, • s(θ) oﬀer oﬀer oﬀer oﬀer oﬀer
- 34. Characteristics of the alternating offer protocol • The utility is increasing in the player’s share and decreasing in time. • This decrease in utility with time is modeled with a discount factor, and . • If a and b receive a share of xa and xb respectively where xa + xb =1, then their utilities at time t are as follows:
- 35. Equilibrium of the alternating offer protocol • If this game is played inﬁnitely overtime, then Rubinstein showed that there is a unique (subgame perfect) equilibrium outcome in which the players immediately reach an agreement on the following shares:
- 36. drawbacks • Rubinstein’s model does not take “deadlines” into account. • There is nothing to prevent the agents from haggling for as long as they wish. • A player’s bargaining power depends on the relative magnitude of the players’ respective costs of haggling. ! • A lot of works on this line have been done.
- 37. Multi-issue Negotiations: Heuristic approaches
- 38. Heuristic approaches • The heuristic approach is particularly useful when there are multiple issues to negotiate, and ﬁnding an equilibrium offer is computationally hard. • Of course there are Game theoretic approaches to multiissue negotiations (e.g. [Fatima2006]). However, here, heuristic approaches are more focusing on computational hardness, complex utilities, etc. • [Fatima2006] S.S.Fatima, M.Wooldridge, and N.R.Jennings, Multi-issue negotiation with deadlines. Journal of Artiﬁcial Intelligence Research, 27:381-417, 2006.
- 39. Monotonic concession [Rosenschein & Zlotkin 94] Rules of Encounter • Players are not allowed to make offers which have a lower utility for their opponent than their last offer. The minimum concession per round can be ﬁxed above 0 => It guarantees to terminate. But, anyway, they have to concede. • Question: how to make concessions? • • • If I do not know the opponents preferences If there are multiple issues Note: In multi-issue negotiations with unknown opponent preferences, it is not always possible to make monotonic concessions
- 40. Time dependent concession • Suppose we have a buyer (the case of the seller is symmetrical) which desires to buy a good for an aspiration price Pmin and reservation price Pmax (highest he is willing to pay); deadline is a time Tmax • Price offered at time t will be: ! • P(t ) = Pmin + F (t )( Pmax − Pmin ) F(t) gives the fraction of the distance left between the ﬁrst (best) offer and the reservation value 1/ β ' min(t , Tmax ) $ " F (t ) = k a + (1 − k a )% % " Tmax & #
- 41. F 1 Conceder (β>1) Linear (β=1) Boluware (β<1) Time Ka Tmax T0 (deadline) 1/ β ' min(t , Tmax ) $ " F (t ) = k a + (1 − k a )% % " Tmax & # ka is constant
- 42. Time dependent concession • Hard-headed (β->0): No concessions, sticks to the initial offer throughout (the opponent may concede, though) • Linear time-dependent concession (β=1): Concession is linear in the time remaining until the deadline • Boulware (β<1): Concedes very slowly; initial offer is maintained until just before the deadline • Conceder (β>1): Concedes to the reservation value very quickly ! • Tit-for-tat : Cooperating on the ﬁrst move and then mirroring whatever the other player did in the preceding round
- 43. Multi-issue negotiations • Single issue negotiations • • Example: seller and buyer for a bottle of wine negotiating over a price Multi-issue negotiations • Example: seller and buyer negotiating for a house over multiple issues, price, place, style, architecture, etc. • Trade-off between issues : An agent can make concessions in one or more issues in order to extract concessions in other issues preferable to him/her • Example • Buyer concede about style instead of proposing nicer place. • Seller concede about price instead of proposing un-preferred place.
- 44. Bidding Based Protocol for Multiple Interdependent Issue Negotiations Takayuki Ito#* ! Collaborative work with Mark Klain*, Hiromitsu Hattori+, and Katsuhide Fujita# ! #Nagoya Institute of Technology, JAPAN ! *Sloan School of Management, Massachusetts Institute of Technology, USA ! +Kyoto University, JAPAN
- 45. Summary Target : Multi-issue Negotiation Protocol! Negotiation with multiple interdependent issues! Non-linearity of agent’s utility functions! Approach : Biding-based Negotiation Protocol! An agent bids conditions to obtain better utility as a bid! Intractability of bid-generation! Result : Outperform protocols applied in liner domains! Difﬁculty in scalability
- 46. [Preliminaries] Modeling Non-linear Utilities Bumpy non-linear utility space! The utility is a summation of satisﬁed contracts’ values Many constraints are satisfied A few/no constraints are satisfied Existing protocols assuming linear utility functions are not effective. How to obtain a solution with high social welfare for non-linear utility function ?
- 47. [Preliminaries] Non-linear Utilities Non-linear utility space! m issues with the domain of integers [0, X]! Issues are common for agents.! A contract is a vector of issue values s = (s1,...,sm).! Agent’s utility function! The function is represented in terms of constraints.! A constraint represents an acceptable region and its value (utility).
- 48. Bidding-based Negotiation Protocol Sampling --- Bid-generation --- Winner determination! An agent submits bids to an mediator for high individual utility. An agent samples its utility space to find high-utility region. Trade-off between high-utility and the limit of # of samples. Samples do NOT always lie on optimal contracts. How to detect better contract regions ?
- 49. Adjusting Samples An agent adjusts samples based on simulated annealing method.! Multiple simulated annealing in the utility space! All random sampling points are initial solutions.! ! ! ! ! ! ! Each sampling point may move to each close optimal contract.
- 50. Bid-generation A bid is deﬁned as a set of contracts which can offer the same utility around an adjusted sampling point.! An agent can submit a bid iff its utility is larger than the threshold. Collect all constraints satisfied by this point Find the intersection of the constraints Several contracts could be submitted as one bid.
- 51. Winner Determination The mediator identiﬁes the combinations of bids as the ﬁnal contract.! The ﬁnal contract is a consistent bids with the highest social welfare.! Only one bid from each agent is included. 1. Find mutually consistent bids Specifying overlapping contract region Agent 1 The final contract 2. Select the best contracts Comparing the summed bid values Agent 2
- 52. Experiments Setting! Constraints satisfying many issues could have larger weights.! The maximum value for a constraint: 100 x # of issues e.g., the possible value for a binary constraint is 200.! Agents have the same issues and domain for each issue value.! Domain for issue value is [0,9]! Approximate search-based winner determination! The ﬁnal contract is searched by the simulated annealing.! The annealer for sample adjustment does not run too long.! The purpose of the sample adjustment is to ﬁnd the peak of the optimum nearest point.
- 53. Experiments Linear utility function case! Comparison between the optimal result and the result of Hill Climbing protocol (for each issue)! ! Issues ! 1 2 3 4 5 6 7 8 9 10 ! HC 0.973 0.991 0.998 0.989 0.986 0.987 0.986 0.996 0.988 0.991 ! Optimality with linear utility function (4 agents) The simple HC protocol can produce nearly optimal results even for a large space.! The mediator can ﬁnd the best value for issue 1, then issue 2, ...
- 54. Experiments Hill Climbing / Bidding-based method for non-linear utility function! HC mediator tends to converge to a local optimum. ! AR mediator has more chances to ﬁnd better contract because agents can generate bids covering multiple optima. 1.2 Optimality Rate 1 0.8 0.6 0.4 HC AR 0.2 2 3 4 5 6 7 Number of Issues 8 9 10
- 55. Deﬁnition of Optimality Rate Optimum contract Sum of all agents’ utility functions and use the Simulated Annealing (SA) to ﬁnd the contract with the highest possible social welfare. ! Optimality Rate = (Optimum solution in the mechanism) / (Optimum contract)
- 56. Experiments Hill Climbing / Bidding-based method for non-linear utility function! HC mediator can quickly obtain the ﬁnal contract. ! AR mediator takes more time, but the ﬁnal contract is calculated within a practical time. 4500 AR 3500 CPU time [ms] 4000 HC 3000 2500 2000 1500 1000 500 0 2 3 4 5 6 7 Number of Issues 8 9 10
- 57. Scalability Optimality Rate The impact of the scaling-up of the problem space! 90%+ optimality for up to 8 issues 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2 3 4 Number of Agents 5 10 9 8 7 6 5 4 3 Number of Issues 2
- 58. Optimality v.s. Sampling Rate 1.2 100 300 500 700 1.15 200 900 Optimality Rate 1.1 1.05 1 0.95 0.9 0.85 2 3 4 5 6 7 Number of Issues 8 9 10
- 59. Sampling Rates v.s. Agreement The Failure rate, % of negotiations that do not lead to an agreement, is higher when there are more sampling points Reason: ! When there are many sampling points, each agent has a better chance of ﬁnding good local optima in its utility space.! However, the num. of bids is limited for computation time.! This increases a risk of not ﬁnding an overlap between the bids
- 60. Discussion The number of bids is ...! # of ! issues 2 3 4 5 6 7 8 9 10 11 12 13 14 15 # of! ! bids 54 200 461 758 1074 1341 1636 1746 1972 2086 2238 2326 2491 2648 The winner determination computation grows exponentially as (# of bids per agent)# of agents! If we use an exhaustive search method (with branch cutting), the problem size is limited to the small one.! The trade-off between the computation time and the optimality
- 61. Summary An bidding-based protocol for the negotiation with multiple interdependent issues.! Our bidding-based protocol outperforms existing protocols applied in linear problems.
- 62. ANAC overview • This competition brings together researchers from the negotiation community and provides a unique benchmark for evaluating practical negotiation strategies in multiissue domains. The three previous competitions have spawned novel research in AI in the ﬁeld of autonomous agent design which are available to the wider research community. • The declared goals of the competition are: • to encourage the design of practical negotiation agents that can proﬁciently negotiate against unknown opponents and in a variety of circumstances, • to provide a benchmark for objectively evaluating different negotiation strategies, • to explore different learning and adaptation strategies and opponent models, and • to collect state-of-the-art negotiating agents and negotiation scenarios, and making them available to the wider research community.
- 63. ANAC 2010-2013 • • Competitions • ANAC2010 Toronoto, Canada ANAC2010 ANAC2011 Agents 7 18 • ANAC2011 Taipei, Taiwan Domains 3 8 • ANAC2012 Valencia, Spain Rules Discount1Factor ( • ANAC2013, Saint Paul, USA ! Organizers • Tim Baarslag, Delft University of Technology • Kobi Gal, Ben-Gurion University • Enrico Gerding, University of Southampton • Koen Hindriks, Delft University of Technology • Takayuki Ito, Nagoya Institute of Technology • Nicholas R. Jennings, University of Southampton • Catholijn Jonker, Delft University of Technology • Sarit Kraus, University of Maryland and Bar-Ilan University • Raz Lin, Bar-Ilan University • Valentin Robu, University of Southampton • Colin R. Williams, University of Southampton ANAC2012 ANAC2013 17 19 24 24 Reserva8on1Value Bid1History
- 64. GENIUS: Tournament Environment • A research tool for automated multi-issue negotiation • Negotiation tournaments in different scenarios • analytical toolbox • Simpliﬁes and supports agent development • repositories of domains and agents • Education : teach students to design negotiation algorithms ! • Programming is all in Java. http://mmi.tudelft.nl/negotiation/index.php/Genius
- 65. Negotiation Domains • Agents negotiate based on negotiation domain which has multiple issues. Utility spaces are not known Example of Bid (fashion style) sweaters Pants classic pants Shoes boots Accessories hat Utility(A) 1.0 Utility(B) Utility(AgentB) Shirts ? Utility(AgentA) • Large variety of domain characteristics possible, and easy to identify Laptop Grocery Energy Number of issues 3 issues 5 issues 8 issues Size 27 1600 390625 Opposition Weak Medium Strong
- 66. Creating an Agent • Implementation itself is very easy if you know Java • extend negotiator.Agent class • override the three methods: • ReceiveMessage() • init() • chooseAction() • Create a package, compile them, and load the main class. • See More details in userguide.pdf
- 67. ANAC2014 • Coming soon! • http:/ /www.itolab.nitech.ac.jp/ANAC2014 • Registration will start from February - March 2014.
- 68. Summary • Part 1: Introduction of Automated Negotiation • Part 2: Bargaining : Game Theoretic Approaches • Part 3: Multi-issue Negotiation : Heuristic Approaches • Part 4: Automated Negotiating Agent Competition
- 69. References (1) • I. Rahwan and S. Fatima, “Negotiations”, Chapter 4 in the Book “Multiagent Systems: 2nd edition” edited by G. Weiss, MIT Press, ISBN 978-0-262-01889-0, 2013. (Recommended) • N. R. Jennings, P. Faratin, A. R. Lomuscio, S. Parsons, C. Sierra and M. Wooldridge, Automated Negotiation: Prospects, Methods and Challenges, International Journal of Group Decision and Negotiation, 10(2):199-215, 2001 • J.F. Nash, The bargaining problem, Econometrica, 18:155-162, 1950 • J.F. Nash, Two-person cooperative game, Econometrica, 21:128-140, 1953 • A. Rubinstein, Perfect equilibrium in a bargaining model. Econometrica, 50(1):97-109, Jan 1982. • A. Rubinstein, A bargaining model with incomplete information about time preference. Econometrica, 53:1151-1172, Jan 1985. • Howard Raiffa, The art and science of negotiation, Harvard Univ. Press, 1982 • M.J. Osborne, A. Rubinstein, Bargaining and Markets, Academic Press, 1990. • J.S. Rosenschein, G. Zlotkin, Rules of encounter, MIT Press, 1994. • Roger B. Myerson, Game Theory: Analysis of Conﬂict, Harvard University Press, 1997. • Sarit Kraus, Strategic Negotiation in Multi-Agent Environments, MIT Press, 2001. • P. Faratin, C. Sierra, and N. R. Jennings. Negotiation decision functions for autonomous agents. Int. Journal of Robotics and Autonomous Systems, 24(3-4):159-182, 1998. • Catholijn Jonker and Valentin Robu. Automated multi-attribute negotiation with efﬁcient use of incomplete preference information. In 3rd Int. Conf. on Autonomous Agents & Multi Agent Systems (AAMAS), New York, pages 1056-1063, 2004
- 70. References (2) • Guoming Lai, Katia Sycara, and Cuihong Li. A decentralized model for multi-attribute negotiations with incomplete information and general utility functions. In Proc. of RRS’06, Hakodate, Japan, 2006. • V. Robu, D.J.A. Somefun, and J. A. La Poutré. Modeling complex multi-issue negotiations using utility graphs. In Proc. of the 4th Int. Conf. on Autonomous Agents & Multi Agent Systems (AAMAS), Utrecht, 2005, • Tim Baarslag, Katsuhide Fujita, Enrico Gerding, Koen Hindriks, Takayuki ITO, Nick R. Jennings, Catholijn Jonker, Sarit Kraus, Raz Lin, Valentin Robu, Colin Williams, The First International Automated Negotiating Agents Competition, Artiﬁcial Intelligence Journal (AIJ), ELSEVIER, 2013. (About ANAC) • Katsuhide Fujita, Takayuki ITO, Mark Klein "Efﬁcient issue-grouping approach for multiple interdependent issues negotiation between exaggerator agents", Decision Support Systems, 2013. • Miguel Angel Lopez Carmona, Iván Marsá Maestre, Mark Klein, Takayuki ITO "Addressing Stability Issues in Mediated Complex Contract Negotiations for Constraint-based, Non-monotonic Utility Spaces", Journal of Autonomous Agents and Multi-Agent Systems (JAAMAS), 3 December 2010. • Takayuki Ito, Mark Klein, Hiromitsu Hattori, "Multi-issue Negotiation Protocol for Agents: Exploring Nonlinear Utility Spaces", In the Proceedings of IJCAI2007, Hyderabad, India, January 6-12, pp. 1347- 1352, 2007.
- 71. Questions / Comments • E-mail : ito@nitech.ac.jp

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