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Bayesian repeated games and reputation

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  • Francoise Forges

    () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique, LEDa - Laboratoire d'Economie de Dauphine - Université Paris-Dauphine)

  • Antoine Salomon

    () (LEDa - Laboratoire d'Economie de Dauphine - Université Paris-Dauphine, LEM - Laboratoire d'Économie Moderne - UP2 - Université Panthéon-Assas)

Abstract

The folk theorem characterizes the (subgame perfect) Nash equilibrium payoffs of an undiscounted or discounted infinitely repeated game - with fully informed, patient players - as the feasible individually rational payoffs of the one-shot game. To which extent does the result still hold when every player privately knows his own payoffs ? Under appropriate assumptions (private values and uniform punishments), the Nash equilibria of the Bayesian infinitely repeated game without discounting are payoff equivalent to tractable, completely revealing, equilibria and can be achieved as interim cooperative solutions of the initial Bayesian game. This characterization does not apply to discounted games with sufficiently patient players. In a class of public good games, the set of Nash equilibrium payoffs of the undiscounted game can be empty, while limit (perfect Bayesian) Nash equilibrium payoffs of the discounted game, as players become infinitely patient, do exist. These equilibria share some features with the ones of multi-sided reputation models.

Suggested Citation

  • Francoise Forges & Antoine Salomon, 2014. "Bayesian repeated games and reputation," Working Papers hal-00803919, HAL.
  • Handle: RePEc:hal:wpaper:hal-00803919
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00803919v5
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    References listed on IDEAS

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    Cited by:

    1. Françoise Forges & Ulrich Horst & Antoine Salomon, 2016. "Feasibility and individual rationality in two-person Bayesian games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 11-36, March.

    More about this item

    Keywords

    reputation; Bayesian game; incentive compatibility; individual rationality; infinitely repeated game; private values; public good; reputation.;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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