A sequential model of bargaining in logic programming

Abstract

This paper proposes a sequential model of bargaining specifying reasoning processes of an agent behind bargaining procedures. We encode agents’ background knowledge, demands, and bargaining constraints in logic programs and represent bargaining outcomes in answer sets. We assume that in each bargaining situation, each agent has a set of goals to achieve, which are normally unachievable without an agreement among all the agents who are involved in the bargaining. Through an alternating-offers procedure, an agreement among bargaining agents may be reached by abductive reasoning. We show that the procedure converges to a Nash equilibrium if each agent makes rational offers/counteroffers in each round. In addition, the sequential model also has a number of desirable properties, such as mutual commitments, individual rationality, satisfactoriness, and honesty.

Keywords

bargaining / logic programming / sequential model / abduction

References

[1] Osborne M J and Rubinstein A. Bargaining and Markets, New York: Academic Press, 1990

[2] Jennings N R, Faratin P, Lomuscio A R, Parsons S, Sierra C, Wooldridge M. Automated negotiation: prospects, methods and challenges. Group Decision and Negotiation, 2001, 10(2): 199-215

[3] Ghosh A, Kale S, Lang K J, Moseley B. Bargaining for revenue shares on tree trading networks. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence. 2013, 129-135

[4] Baarslag T, Hindriks K V. Accepting optimally in automated negotiation with incomplete information. In: Proceedings of the 12th International Conference on Autonomous Agents and Multi-Agent Systems. 2013, 715-722

[5] Kraus S, Sycara K P, Evenchik A. Reaching agreements through argumentation: a logical model and implementation. Artificial Intelligence, 1998, 104(1-2): 1-69

[6] Zhang D. A Logical Model of Nash Bargaining Solution. In: Proceed ings of the 19th International Joint Conference on Artificial Intelligence. 2005, 983-990

[7] Zhang D, Zhang Y. A computational model of logic-based negotiation. In: Proceedings of the 21st National Conference on Artificial Intelligence. 2006, 728-733

[8] Zhang D. Reasoning about bargaining situations. In: Proceedings of the 22nd National Conference on Artificial Intelligence. 2007, 154-160

[9] Son T C, Sakama C. Negotiation using logic programming with consistency restoring rules. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence. 2009, 930-935

[10] Zhang D. A logic-based axiomatic model of bargaining. Artificial Intelligence, 2010, 174(16-17): 1307-1322

[11] Son T C, Pontelli E, Nguyen N, Sakama C. Formalizing negotiations using logic programming. ACM Transactions on Computational Logic, 2014, 15(2): 12

[12] Jing X, Zhang D, Luo X. A logical framework of bargaining with integrity constraints. In: Proceedings of the 26th Australasian Conference on Artificial Intelligence. 2013, 1-13

[13] John F, Nash J F. The bargaining problem. Econometrica, 1950, 18(2): 155-162

[14] Zhang D, Zhang Y. An ordinal bargaining solution with fixed-point property. Journal of Artificial Intelligence Research, 2008, 33: 433-464

[15] Kakas A C, Kowalski R A, Toni F. Abductive logic programming. Journal of Logic and Computation, 1992, 2(6): 719-770

[16] Kakas A C, Kowalski R A, Toni F. The role of abduction in logic programming. Handbook of Logic in AI and Logic Programming, 1998, 5: 235-324

[17] Sadri F, Toni F, Torroni P. An abductive logic programming architecture for negotiating agents. In: Proceedings of the 8th European Conference on Logics in Artificial Intelligence. 2002, 419-431

[18] Lin F Z, You J H. Abductive logic programming by nonground rewrite systems. In: Proceedings of the 23rd National Conference on Artificial Intelligence. 2008, 480-485

[19] Gelfond M, Lifschitz V. Classical negation in logic programs and disjunctive databases. New Generation Computing, 1991, 9(3-4): 365-386

[20] Lifschitz V. Foundations of logic programming. Principles of Knowledge Representation, 1996, 3: 69-127

[21] Gelfond M, Lifschitz V. The stable model semantics for logic programming. In: Proceedings of the 5th Joint International Logic Programming Conference and Symposium. 1988, 1070-1080

[22] Osborne MJ, Rubinstein A. A Course in Game Theory. Massachusetts: MIT Press, 1994

[23] Huang W, Zhang D, Zhang Y, Perrussel L. Bargain over joint plans. In: Proceedings of the 11th Pacific Rim International Conference on Artificial Intelligence. 2010, 608-613

[24] Son T C, Sakama C, Pontelli E. Logic programming for multiagent planning with negotiation. Lecture Notes in Computer Science, 2009, 5649: 99-114

[25] Ragone A, Noia T D, Sciascio E D, Donini F M. Description logics for multi-issue bilateral negotiation with incomplete information. In: Proceedings of the 22nd National Conference on Artificial Intelligence. 2007, 477-482

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg