Discounted Repeated Games with General Incomplete Information

We analyze discounted repeated games with incomplete information, and such that the payoffs of the players depend only on their own type (known-own payoff case). We describe an algorithm to find all equilibrium payoffs in games for which there exists an open set of belief-free equilibria of Horner 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 Nash equilibrium payoffs can be approximated 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 equilibrium payoffs in repeated games without discounting, and it is also larger than the set of payoffs obtained in belief-free equilibria. The results are illustrated on bargaining and oligopoly examples.