Abstract
Graphical Games are a succinct representation of multi agent interactions in which each participant interacts with a limited number of other agents. The model resembles Distributed Constraint Optimization Problems (DCOPs) including agents, variables, and values (strategies). However, unlike distributed constraints, local interactions of Graphical Games take the form of small strategic games and the agents are expected to seek a Nash Equilibrium rather than a cooperative minimal cost joint assignment.
The present paper models graphical games as a Distributed Constraint Satisfaction Problem with unique k-ary constraints in which each agent is only aware of its part in the constraint. A proof that a satisfying solution to the resulting problem is an ε-Nash equilibrium is provided and an Asynchronous Backtracking algorithm is proposed for solving this distributed problem. The algorithm’s completeness is proved and its performance is evaluated.
The research was supported by the Lynn and William Frankel Center for Computer Sciences at Ben-Gurion University and by the Paul Ivanier Center for Robotics Research and Production Management.
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References
Apt, K.R., Rossi, F., Venable, K.B.: A comparison of the notions of optimality in soft constraints and graphical games. CoRR, abs/0810.2861 (2008)
Bessière, C., Maestre, A., Brito, I., Meseguer, P.: Asynchronous backtracking without adding links: a new member in the ABT family. Artif. Intell. 161(1-2), 7–24 (2005)
Brito, I., Meisels, A., Meseguer, P., Zivan, R.: Distributed constraint satisfaction with partially known constraints. Constraints 14(2), 199–234 (2009)
Ceppi, S., Gatti, N., Patrini, G., Rocco, M.: Local search techniques for computing equilibria in two-player general-sum strategic-form games. In: 9th Intl. Conf. on Autonomous Agents and Multiagent Systems, AAMAS 2010, pp. 1469–1470 (2010)
Chapman, A.C., Farinelli, A., de Cote, E.M., Rogers, A., Jennings, N.R.: A distributed algorithm for optimising over pure strategy nash equilibria. In: Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2010, Atlanta, Georgia, USA (July 2010)
Ganzfried, S., Sandholm, T.: Computing equilibria by incorporating qualitative models. In: 9th Intl. Conf. on Autonomous Agents and Multiagent Systems, AAMAS 2010, pp. 183–190 (2010)
Grubshtein, A., Zivan, R., Meisels, A., Grinshpoun, T.: Local search for distributed asymmetric optimization. In: 9th Intl. Conf. on Autonomous Agents and Multi-Agent Systems, AAMAS 2010, Toronto, Canada, pp. 1015–1022 (May 2010)
Kearns, M.J., Littman, M.L., Singh, S.P.: Graphical models for game theory. In: UAI 2001: 17th Conference in Uncertainty in Artificial Intelligence, San Francisco, CA, USA, pp. 253–260 (2001)
Lutati, B., Gontmakher, I., Lando, M.: AgentZero – a framework for executing, analyzing and developing DCR algorithms, http://code.google.com/p/azapi-test/
Maheswaran, R.T., Pearce, J.P., Tambe, M.: Distributed algorithms for DCOP: A graphical-game-based approach. In: Proceedings of Parallel and Distributed Computing Systems, PDCS 2004, pp. 432–439 (September 2004)
Meisels, A.: Distributed Search by Constrained Agents: Algorithms, Performance, Communication. Springer (2007)
Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press (2007)
Ortiz, L.E., Kearns, M.J.: Nash propagation for loopy graphical games. In: NIPS 2002: Advances in Neural Information Processing Systems 15, Vancouver, British Columbia, Canada, pp. 793–800 (2002)
Osborne, M.J., Rubinstein, A.: A Course in Game Theory. The MIT Press (1994)
Porter, R., Nudelman, E., Shoham, Y.: Simple search methods for finding a nash equilibrium. Games and Economic Behavior 63(2), 642–662 (2008)
Sandholm, T., Gilpin, A., Conitzer, V.: Mixed-integer programming methods for finding nash equilibria. In: 20th National Conference on Artificial Intelligence, AAAI 2005, vol. 2, pp. 495–501. AAAI Press (2005)
Soni, V., Singh, S.P., Wellman, M.P.: Constraint satisfaction algorithms for graphical games. In: 6th International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2007, Honolulu, Hawaii, USA, p. 67 (May 2007)
Yokoo, M., Durfee, E.H., Ishida, T., Kuwabara, K.: Distributed constraint satisfaction problem: Formalization and algorithms. IEEE Trans. on Data and Kn. Eng. 10, 673–685 (1998)
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Grubshtein, A., Meisels, A. (2012). Finding a Nash Equilibrium by Asynchronous Backtracking. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_66
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DOI: https://doi.org/10.1007/978-3-642-33558-7_66
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