Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 3
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Chan, Chi-Kong Hao, Jianye and Leung, Ho-Fung 2017. Reciprocal Social Strategy in Social Repeated Games and Emergence of Social Norms. International Journal on Artificial Intelligence Tools, Vol. 26, Issue. 01, p. 1760007.
    Zhou, Luowei Yang, Pei Chen, Chunlin and Gao, Yang 2017. Multiagent Reinforcement Learning With Sparse Interactions by Negotiation and Knowledge Transfer. IEEE Transactions on Cybernetics, Vol. 47, Issue. 5, p. 1238.
    Chan, Chi-Kong Hao, Jianye and Leung, Ho-fung 2015. Reciprocal Social Strategy in Social Repeated Games. p. 966.
    ×
  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register Recommend to librarian

Repeated games for multiagent systems: a survey

  • Andriy Burkov (a1) and Brahim Chaib-Draa (a1)
Abstract

Repeated games are an important mathematical formalism to model and study long-term economic interactions between multiple self-interested parties (individuals or groups of individuals). They open attractive perspectives in modeling long-term multiagent interactions. This overview paper discusses the most important results that actually exist for repeated games. These results arise from both economics and computer science. Contrary to a number of existing surveys of repeated games, most of which originated from the economic research community, we are first to pay a special attention to a number of important distinctive features proper to artificial agents. More precisely, artificial agents, as opposed to the human agents mainly aimed by the economic research, are usually bounded whether in terms of memory or performance. Therefore, their decisions have to be based on the strategies defined using finite representations. Furthermore, these strategies have to be efficiently computed or approximated using a limited computational resource usually available to artificial agents.

Copyright
COPYRIGHT: © Cambridge University Press 2013 
References
Hide All
Abreu, D. 1986. Extremal equilibria of oligopolistic supergames. Journal of Economic Theory 39(1), 191–225.
Abreu, D. 1988. On the theory of infinitely repeated games with discounting. Econometrica 56, 383–396.
Abreu, D., Pearce, D., Stacchetti, E. 1990. Toward a theory of discounted repeated games with imperfect monitoring. Econometrica 58(5), 1041–1063.
Abreu, D., Rubinstein, A. 1988. The structure of Nash equilibrium in repeated games with finite automata. Econometrica 56(6), 1259–1281.
Aumann, R. 1981. Survey of repeated games. Essays in Game Theory and Mathematical Economics in Honor of Oskar Morgenstern, 11–42.
Aumann, R., Maschler, M., Stearns, R. 1995. Repeated Games With Incomplete Information. The MIT press.
Aumann, R., Shapley, L. 1994. Long term competition: a game theoretic analysis. Essays in Game Theory in Honor of Michael Maschler, 1–15.
Banerjee, B., Peng, J. 2003. Adaptive policy gradient in multiagent learning. In Proceedings of the Second International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS'03). ACM Press, 686–692.
Banks, J., Sundaram, R. 1990. Repeated games, finite automata, and complexity. Games and Economic Behavior 2(2), 97–117.
Ben-Porath, E. 1990. The complexity of computing a best response automaton in repeated games with mixed strategies. Games and Economic Behavior 2(1), 1–12.
Ben-Porath, E. 1993. Repeated games with finite automata. Journal of Economic Theory 59, 17–39.
Ben-Porath, E., Peleg, B. 1987. On the Folk Theorem and Finite Automata. Mimeo, Hebrew University of Jerusalim.
Ben-Sasson, E., Kalai, A. T., Kalai, E. 2007. An approach to bounded rationality. In Advances in Neural Information Processing Systems 19, Schisölkopf, B., Platt J. & Hoffman, T. (eds). MIT Press, 145–152.
Benoit, J.-P., Krishna, V. 1985. Finitely repeated games. Econometrica 53(4), 905–922.
Benoit, J.-P., Krishna, V. 1999. The Folk Theorems for Repeated Games: A Synthesis. Mimeo, Pennsylvania State University.
Bernstein, D., Givan, R., Immerman, N., Zilberstein, S. 2003. The complexity of decentralized control of Markov decision processes. Mathematics of Operations Research 27(4), 819–840.
Berry, D., Fristedt, B. 1985. Bandit Problems. Chapman and Hall London.
Bhaskar, V., Obara, I. 2002. Belief-based equilibria in the repeated Prisoners’ Dilemma with private monitoring. Journal of Economic Theory 102(1), 40–69.
Borgs, C., Chayes, J., Immorlica, N., Kalai, A., Mirrokni, V., Papadimitriou, C. 2008. The myth of the folk theorem. In Proceedings of the 40th Annual ACM Symposium on Theory of Computing (STOC'08). ACM Press, 365–372.
Bowling, M., Veloso, M. 2002. Multiagent learning using a variable learning rate. Artificial Intelligence 136(2), 215–250.
Burkov, A., Chaib-draa, B. 2009. Effective learning in the presence of adaptive counterparts. Journal of Algorithms 64(4), 127–138.
Burkov, A., Chaib-draa, B. 2010. An approximate subgame-perfect equilibrium computation technique for repeated games. In Proceedings of Twenty-Fourth AAAI Conference on Artificial Intelligence (AAAI'10). AAAI Press, 729–736.
Chen, X., Deng, X. 2006. Settling the complexity of two-player Nash equilibrium. In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06). IEEE Computer Society, 261–272.
Cheng, S., Reeves, D., Vorobeychik, Y., Wellman, M. 2004. Notes on equilibria in symmetric games. In AAMAS-04 Workshop on Game-Theoretic and Decision-Theoretic Agents.
Compte, O. 1998. Communication in repeated games with imperfect private monitoring. Econometrica 66(3), 597–626.
Conitzer, V., Sandholm, T. 2007. AWESOME: a general multiagent learning algorithm that converges in self-play and learns a best response against stationary opponents. Machine Learning 67(1), 23–43.
Cronshaw, M. 1997. Algorithms for finding repeated game equilibria. Computational Economics 10(2), 139–168.
Cronshaw, M., Luenberger, D. 1994. Strongly symmetric subgame perfect equilibria in infinitely repeated games with perfect monitoring and discounting. Games and Economic Behavior 6(2), 220–237.
Daskalakis, C., Goldberg, P., Papadimitriou, C. 2006. The complexity of computing a Nash equilibrium. In Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing (STOC'06). ACM Press, 71–78.
Ely, J., Hörner, J., Olszewski, W. 2005. Belief-free equilibria in repeated games. Econometrica 73(2), 377–415.
Ely, J., Valimaki, J. 2002. A robust folk theorem for the prisoner's dilemma. Journal of Economic Theory 102(1), 84–105.
Friedman, J. 1971. A non-cooperative equilibrium for supergames. The Review of Economic Studies, 1–12.
Fudenberg, D., Kreps, D., Maskin, E. 1990. Repeated games with long-run and short-run players. The Review of Economic Studies 57(4), 555–573.
Fudenberg, D., Levine, D. 1991. An approximate folk theorem with imperfect private information. Journal of Economic Theory 54(1), 26–47.
Fudenberg, D., Levine, D., Maskin, E. 1994. The folk theorem with imperfect public information. Econometrica 62(5), 997–1039.
Fudenberg, D., Levine, D., Takahashi, S. 2007. Perfect public equilibrium when players are patient. Games and Economic Behavior 61(1), 27–49.
Fudenberg, D., Tirole, J. 1991. Game Theory. MIT Press.
Gilboa, I. 1988. The complexity of computing best-response automata in repeated games. Journal of economic theory 45(2), 342–352.
Gossner, O., Tomala, T. 2009. Repeated games. Encyclopedia of Complexity and Systems Science, forthcoming.
Hart, S., Mansour, Y. 2007. The communication complexity of uncoupled Nash equilibrium procedures. In Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing (STOC'07). ACM Press, 345–353.
Hörner, J., Lovo, S. 2009. Belief-free equilibria in games with incomplete information. Econometrica 77(2), 453–487.
Hörner, J., Olszewski, W. 2006. The folk theorem for games with private almost-perfect monitoring. Econometrica 74(6), 1499–1544.
Hörner, J., Olszewski, W. 2007. How robust is the folk theorem with imperfect public monitoring. Northwestern University.
Jong, S., Tuyls, K., Verbeeck, K. 2008. Fairness in multi-agent systems. The Knowledge Engineering Review 23(2), 153–180.
Judd, K., Yeltekin, S., Conklin, J. 2003. Computing supergame equilibria. Econometrica 71(4), 1239–1254.
Kaelbling, L., Littman, M., Cassandra, A. 1998. Planning and acting in partially observable stochastic domains. Artificial Intelligence 101(1–2), 99–134.
Kalai, E., Stanford, W. 1988. Finite rationality and interpersonal complexity in repeated games. Econometrica 56(2), 397–410.
Kandori, M., Obara, I. 2006. Efficiency in repeated games revisited: the role of private strategies. Econometrica 74(2), 499–519.
Kreps, D., Wilson, R. 1982. Sequential equilibria. Econometrica: Journal of the Econometric Society, 863–894.
Kushilevitz, E., Nisan, N. 1997. Communication Complexity. Cambridge University Press.
Laraki, R. 2002. Repeated games with lack of information on one side: the dual differential approach. Mathematics of Operations Research 27(2), 419–440.
Lehrer, E., Pauzner, A. 1999. Repeated games with differential time preferences. Econmetrica 67(2), 393–412.
Lehrer, E., Yariv, L. 1999. Repeated games with incomplete information on one side: the case of different discount factors. Mathematics of Operations Research 24(1), 204–218.
Lipman, B., Wang, R. 2000. Switching costs in frequently repeated games. Journal of Economic Theory 93(2), 149–190.
Lipman, B., Wang, R. 2009. Switching costs in infinitely repeated games. Games and Economic Behavior 66(1), 292–314.
Littman, M., Stone, P. 2005. A polynomial-time Nash equilibrium algorithm for repeated games. Decision Support Systems 39(1), 55–66.
Mailath, G., Matthews, S., Sekiguchi, T. 2002. Private strategies in finitely repeated games with imperfect public monitoring. Contributions to Theoretical Economics 2(1), 1046.
Mailath, G., Morris, S. 2002. Repeated games with almost-public monitoring. Journal of Economic Theory 102(1), 189–228.
Mailath, G., Samuelson, L. 2006. Repeated Games and Reputations: Long-run Relationships. Oxford University Press.
Matsushima, H. 2004. Repeated games with private monitoring: two players. Econometrica 72(3), 823–852.
Mertens, J., Sorin, S., Zamir, S. 1994. Repeated games, Part A: background material. CORE Discussion Papers, 9420.
Myerson, R. 1991. Game Theory: Analysis of Conflict. Harvard University Press.
Nash, J. 1950. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America 36(1), 48–49.
Neme, A., Quintas, L. 1995. Subgame perfect equilibrium of repeated games with implementation costs. Journal of Economic Theory 66(2), 599–608.
Neyman, A. 1985. Bounded complexity justifies cooperation in the finitely repeated Prisoner's Dilemma. Economics Letters 19(3), 227–229.
Neyman, A. 1995. Cooperation, repetition, and automata. In Cooperation: Game Theoretic Approaches, volume 155 of NATO ASI Series F. Springer-Verlag, 233–255.
Neyman, A. 1998. Finitely repeated games with finite automata. Mathematics of Operations Research 23(3), 513–552.
Obara, I. 2009. Folk theorem with communication. Journal of Economic Theory 144(1), 120–134.
Osborne, M., Rubinstein, A. 1994. A Course in Game Theory. MIT Press.
Papadimitriou, C. 1992. On players with a bounded number of states. Games and Economic Behavior 4(1), 122–131.
Papadimitriou, C., Yannakakis, M. 1988. Optimization, approximation, and complexity classes. In Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing. ACM Press, 229–234.
Papadimitriou, C., Yannakakis, M. 1994. On complexity as bounded rationality (extended abstract). In Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing. ACM Press, 726–733.
Pearce, D. 1992. Repeated games: cooperation and rationality. In Advances in Economic Theory: Sixth World Congress, vol. 1. Cambridge University Press, 132–174.
Piccione, M. 2002. The repeated prisoner's dilemma with imperfect private monitoring. Journal of Economic Theory 102(1), 70–83.
Radner, R. 1986. Repeated partnership games with imperfect monitoring and no discounting. The Review of Economic Studies 53(1), 43–57.
Ramchurn, S., Huynh, D., Jennings, N. 2004. Trust in multi-agent systems. The Knowledge Engineering Review 19(1), 1–25.
Rasmusen, E. 1994. Games and Information. Blackwell Cambridge.
Renault, J., Scarlatti, S., Scarsini, M. 2005. A folk theorem for minority games. Games and Economic Behavior 53(2), 208–230.
Renault, J., Scarlatti, S., Scarsini, M. 2008. Discounted and finitely repeated minority games with public signals. Mathematical Social Sciences 56(1), 44–74.
Rubinstein, A. 1979. Equilibrium in supergames with the overtaking criterion. Journal of Economic Theory 21(1), 1–9.
Russell, S., Norvig, P. 2009. Artificial Intelligence: A Modern Approach, 3rd edn.Prentice Hall.
Sekiguchi, T. 1997. Efficiency in repeated Prisoner's Dilemma with private monitoring. Journal of Economic Theory 76(2), 345–361.
Sorin, S. 1986. On repeated games with complete information. Mathematics of Operations Research 11(1), 147–160.
Sutton, R. S., Barto, A. G. 1998. Reinforcement Learning: An Introduction. The MIT Press.
Zemel, E. 1989. Small talk and cooperation: a note on bounded rationality. Journal of Economic Theory 49(1), 1–9.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Knowledge Engineering Review
  • ISSN: 0269-8889
  • EISSN: 1469-8005
  • URL: /core/journals/knowledge-engineering-review
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Metrics

Full text views

Total number of HTML views: 6
Total number of PDF views: 29 *
Loading metrics...

Abstract views

Total abstract views: 171 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×