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Repeated games with incomplete information and discounting

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    (University of Toronto)

Abstract

. We analyze discounted repeated games with incomplete information, such that the players' payoffs depend only on their own type (known-own payoff case). We describe an algorithm for finding all equilibrium payoffs in games for which there exists an open set of belief-free equilibria of Hörner and Lovo (2009). This includes generic games with one-sided incomplete information and a large and important class of games with multi-sided incomplete information. When players become sufficiently patient, all Bayesian Nash equilibrium payoffs can be approximated by payoffs in sequential equilibria in which information is revealed finitely many times. The set of equilibrium payoffs is typically larger than the set of equilibrium payoffs in repeated games without discounting, and larger than the set of payoffs obtained in belief-free equilibria. The results are illustrated in bargaining and oligopoly examples.

Suggested Citation

  • ,, 2014. "Repeated games with incomplete information and discounting," Theoretical Economics, Econometric Society, vol. 9(3), September.
    • Handle: RePEc:the:publsh:1390
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    References listed on IDEAS

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    1. Susan Athey & Kyle Bagwell, 2008. "Collusion With Persistent Cost Shocks," Econometrica, Econometric Society, vol. 76(3), pages 493-540, May.
    2. Sergiu Hart, 1985. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 117-153, February.
    3. repec:cor:louvrp:-636 is not listed on IDEAS
    4. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "Learning from private information in noisy repeated games," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1733-1769, September.
    5. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, vol. 71(6), pages 1619-1660, November.
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    Cited by:

    1. Kimmo Berg & Gijs Schoenmakers, 2017. "Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games," Games, MDPI, vol. 8(4), pages 1-14, November.
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    3. Satyajit Chatterjee & Dean Corbae & Kyle Dempsey & José‐Víctor Ríos‐Rull, 2023. "A Quantitative Theory of the Credit Score," Econometrica, Econometric Society, vol. 91(5), pages 1803-1840, September.

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    More about this item

    Keywords

    Repeated games; incomplete information; reputation;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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