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Bayesian repeated games and reputation

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  • Francoise Forges

    ()
    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine, LEDa - Laboratoire d'Economie de Dauphine - Université Paris IX - Paris Dauphine)

  • Antoine Salomon

    ()
    (LEDa - Laboratoire d'Economie de Dauphine - Université Paris IX - Paris Dauphine, LEM - Laboratoire d'Économie Moderne - Université Paris II - Panthéon-Assas : EA4442)

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.

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Paper provided by HAL in its series Working Papers with number hal-00803919.

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Date of creation: 12 Feb 2014
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Handle: RePEc:hal:wpaper:hal-00803919

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

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