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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 learns. We show that there are robust equilibria where players eventually obtain payoffs as if the true state were common knowledge and players played a “belief-free” equilibrium. The result is applied to various examples, including secret pricecutting with unknown demand.

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    File URL: http://economics.sas.upenn.edu/system/files/12-044.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 12-044.

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    Length: 76 pages
    Date of creation: 10 Nov 2012
    Date of revision:
    Handle: RePEc:pen:papers:12-044
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    1. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine.
    2. Shalev Jonathan, 1994. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information and Known-Own Payoffs," Games and Economic Behavior, Elsevier, vol. 7(2), pages 246-259, September.
    3. 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.
    4. George J Mailath & Stephen Morris, 2001. "Repeated Games with Almost-Public Monitoring," Levine's Working Paper Archive 625018000000000257, David K. Levine.
    5. Jeffrey Ely, 2000. "A Robust Folk Theorem for the Prisoners' Dilemma," Econometric Society World Congress 2000 Contributed Papers 0210, Econometric Society.
    6. George J. Mailath & Wojciech Olszewski, 2008. "Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring," PIER Working Paper Archive 08-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. 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.
    8. Drew Fudenberg & David K Levine & Satoru Takahashi, 2004. "Perfect Public Equilibrium When Players are Patient," Levine's Working Paper Archive 618897000000000865, David K. Levine.
    9. William Fuchs, 2007. "Contracting with Repeated Moral Hazard and Private Evaluations," American Economic Review, American Economic Association, vol. 97(4), pages 1432-1448, September.
    10. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2011. "Belief-free equilibria in games with incomplete information: Characterization and existence," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1770-1795, September.
    11. V. Bhaskar & Ichiro Obara, . "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Penn CARESS Working Papers d93eb6f40c65728f9e1a7b114, Penn Economics Department.
    12. Johannes Hörner & Wojciech Olszewski, 2006. "The Folk Theorem for Games with Private Almost-Perfect Monitoring," Econometrica, Econometric Society, vol. 74(6), pages 1499-1544, November.
    13. Wiseman, Thomas, 2012. "A partial folk theorem for games with private learning," Theoretical Economics, Econometric Society, vol. 7(2), May.
    14. Dekel, Eddie & Fudenberg, Drew & Levine, David, 2004. "Learning to Play Bayesian Games," Scholarly Articles 3200612, Harvard University Department of Economics.
    15. David A. Miller, 2005. "The dynamic cost of ex post incentive compatibility in repeated games of private information," Game Theory and Information 0510002, EconWPA.
    16. 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.
    17. Jeffrey C. Ely & Johannes Horner & Wojciech Olszewski, 2003. "Belief-free Equilibria in Repeated Games," Levine's Working Paper Archive 666156000000000367, David K. Levine.
    18. Yamamoto, Yuichi, 2009. "A limit characterization of belief-free equilibrium payoffs in repeated games," Journal of Economic Theory, Elsevier, vol. 144(2), pages 802-824, March.
    19. Fudenberg, Drew & Yamamoto, Yuichi, 2010. "Repeated Games Where the Payoffs and Monitoring Structure Are Unknown," Scholarly Articles 13411374, Harvard University Department of Economics.
    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.
    21. Joseph E. Harrington & Andrzej Skrzypacz, 2011. "Private Monitoring and Communication in Cartels: Explaining Recent Collusive Practices," American Economic Review, American Economic Association, vol. 101(6), pages 2425-49, October.
    22. 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.
    23. repec:ebl:ecbull:v:3:y:2007:i:58:p:1-16 is not listed on IDEAS
    24. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
    25. 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.
    26. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, June.
    27. Michihiro Kandori, 2001. "Introduction to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-114, CIRJE, Faculty of Economics, University of Tokyo.
    28. 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).
    29. Hitoshi Matsushima, 2003. "Repeated Games with Private Monitoring: Two Players," CIRJE F-Series CIRJE-F-242, CIRJE, Faculty of Economics, University of Tokyo.
    30. Thomas Wiseman, 2005. "A Partial Folk Theorem for Games with Unknown Payoff Distributions," Econometrica, Econometric Society, vol. 73(2), pages 629-645, 03.
    31. 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.
    32. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    33. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    34. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
    35. Yamamoto, Yuichi, 2012. "Characterizing belief-free review-strategy equilibrium payoffs under conditional independence," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1998-2027.
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