REPEATED GAMES WITH INCOMPLETE INFORMATION AND DISCOUNTING

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 approx-imated 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 equi-librium 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. 1