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Repeated games with incomplete information on one side

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    (Department of Economics, University of Chicago)

Abstract

This paper studies repeated games with incomplete information on one side and equal discount factors for both players. The payoffs of the informed player I depend on one of two possible states of the world, which is known to her. The payoffs of the uninformed player U do not depend on the state of the world (that is, U knows his payoffs), but player I's behavior makes knowledge of the state of interest to player U. We define a finitely revealing equilibrium as a Bayesian perfect equilibrium where player I reveals information in a bounded number of periods. We define an ICR profile as a strategy profile in which (a) after each history the players have individually rational payoffs and (b) no type of player I wants to mimic the behavior of the other type. We show that when the players are patient, all Nash equilibrium payoffs in the repeated game can be approximated by payoffs in finitely revealing equilibria, which themselves approximate the set of all ICR payoffs. We provide a geometric characterization of the set of equilibrium payoffs, which can be used for computations.

Suggested Citation

  • ,, 2008. "Repeated games with incomplete information on one side," Theoretical Economics, Econometric Society, vol. 3(1), March.
    • Handle: RePEc:the:publsh:240
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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.
    2. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    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.
    4. Sperisen, Benjamin, 2018. "Bounded memory and incomplete information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 382-400.
    5. Golosov, Mikhail & Skreta, Vasiliki & Tsyvinski, Aleh & Wilson, Andrea, 2014. "Dynamic strategic information transmission," Journal of Economic Theory, Elsevier, vol. 151(C), pages 304-341.
    6. Rosenberg, Dinah & Solan, Eilon & Vieille, Nicolas, 2013. "Strategic information exchange," Games and Economic Behavior, Elsevier, vol. 82(C), pages 444-467.
    7. 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.
    8. Peters, Michael, 2015. "Reciprocal contracting," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 102-126.
    9. Nuh Aygün Dalkıran, 2016. "Order of limits in reputations," Theory and Decision, Springer, vol. 81(3), pages 393-411, September.

    More about this item

    Keywords

    Repeated games; incomplete information; discounting;
    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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