Theoretical Economics 3 (2008), 29–84

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### Repeated games with incomplete information on one side

*Marcin Pęski*

#### 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.

Keywords: Repeated games, incomplete information, discounting

JEL classification: C73

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