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Individual Learning and Cooperation in Noisy Repeated Games

  • Yuichi Yamamoto

    ()

    (Department of Economics, University of Pennsylvania)

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    We investigate whether two players in a long-run relationship can maintain cooperation when the details of the underlying game are unknown. Specifically, we consider a new class of repeated games with private monitoring, where an unobservable state of the world influences the payoff functions and/or the monitoring structure. Each player privately learns the state over time but cannot observe what the opponent learned. We show that there are robust equilibria in which players eventually obtain payoffs as if the true state were common knowledge and players played a “belief-free” equilibrium. We also provide explicit equilibrium constructions in various economic examples

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    File URL: http://economics.sas.upenn.edu/system/files/13-038.pdf
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    Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 13-038.

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    Length: 78 pages
    Date of creation: 06 Jul 2013
    Date of revision:
    Handle: RePEc:pen:papers:13-038
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    1. Jeffrey Ely, 2000. "A Robust Folk Theorem for the Prisoners' Dilemma," Econometric Society World Congress 2000 Contributed Papers 0210, Econometric Society.
    2. V. Bhaskar & Ichiro Obara, . "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Penn CARESS Working Papers d93eb6f40c65728f9e1a7b114, Penn Economics Department.
    3. William Fuchs, 2005. "Contracting with Repeated Moral Hazard and Private Evaluations," Discussion Papers 04-012, Stanford Institute for Economic Policy Research.
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    5. Dekel, Eddie & Fudenberg, Drew & Levine, David, 2004. "Learning to Play Bayesian Games," Scholarly Articles 3200612, Harvard University Department of Economics.
    6. Chen, Bo, 2010. "A belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring," Journal of Economic Theory, Elsevier, vol. 145(1), pages 402-420, January.
    7. Joseph E. Harrington, Jr. & Andrzej Skrzypacz, 2009. "Private Monitoring and Communication in Cartels: Explaining Recent Collusive Practices," Economics Working Paper Archive 555, The Johns Hopkins University,Department of Economics.
    8. George Mailath & Stephen Morris, . ""Repeated Games with Almost-Public Monitoring''," CARESS Working Papres 99-09, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
    9. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    10. Yamamoto, Yuichi, 2012. "Characterizing belief-free review-strategy equilibrium payoffs under conditional independence," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1998-2027.
    11. Michihiro Kandori & Ichiro Obara, 2006. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Econometrica, Econometric Society, vol. 74(2), pages 499-519, 03.
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    13. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, March.
    14. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
    15. Thomas Wiseman, 2005. "A Partial Folk Theorem for Games with Unknown Payoff Distributions," Econometrica, Econometric Society, vol. 73(2), pages 629-645, 03.
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    18. repec:ebl:ecbull:v:3:y:2007:i:58:p:1-16 is not listed on IDEAS
    19. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    20. O. Gossner & N. Vieille, 2000. "Strategic Learning in Games with Symmetric Information," THEMA Working Papers 2000-27, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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    22. Johannes Horner & Wojciech Olszewski, 2005. "The Folk Theorem for Games with Private, Almost-Perfect Monitoring," NajEcon Working Paper Reviews 172782000000000006, www.najecon.org.
    23. HART, Sergiu, . "Nonzerosum two-person repeated games with incomplete information," CORE Discussion Papers RP -636, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    24. Wojciech Olszewski, 2007. "A Simple Exposition of Belief-Free Equilibria in Repeated Games," Economics Bulletin, AccessEcon, vol. 3(58), pages 1-16.
    25. Fudenberg, Drew & Yamamoto, Yuichi, 2010. "Repeated Games Where the Payoffs and Monitoring Structure Are Unknown," Scholarly Articles 13411374, Harvard University Department of Economics.
    26. David A. Miller, 2012. "Robust Collusion with Private Information," Review of Economic Studies, Oxford University Press, vol. 79(2), pages 778-811.
    27. Lehrer, E, 1990. "Nash Equilibria of n-Player Repeated Games with Semi-standard Information," International Journal of Game Theory, Springer, vol. 19(2), pages 191-217.
    28. Wiseman, Thomas, 2012. "A partial folk theorem for games with private learning," Theoretical Economics, Econometric Society, vol. 7(2), May.
    29. Fudenberg, D. & Levine, D.K. & Maskin, E., 1989. "The Folk Theorem With Inperfect Public Information," Working papers 523, Massachusetts Institute of Technology (MIT), Department of Economics.
    30. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
    31. Sylvain Chassang, 2010. "Building Routines: Learning, Cooperation, and the Dynamics of Incomplete Relational Contracts," American Economic Review, American Economic Association, vol. 100(1), pages 448-65, March.
    32. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
    33. Yuichi Yamamoto, 2012. "Characterizing Belief-Free Review-Strategy Equilibrium Payoffs under ConditionalIndependence," PIER Working Paper Archive 12-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    34. Rotemberg, Julio J & Saloner, Garth, 1986. "A Supergame-Theoretic Model of Price Wars during Booms," American Economic Review, American Economic Association, vol. 76(3), pages 390-407, June.
    35. Jee-Hyeong Park, 2011. "Enforcing International Trade Agreements with Imperfect Private Monitoring," Review of Economic Studies, Oxford University Press, vol. 78(3), pages 1102-1134.
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