Repeated Games with Uncertain Outcomes

This paper studies repeated games with imperfect public monitoring where the players are uncertain both about the payoff functions and about the relationship between the distribution of signals and the actions played. We introduce the concept of perfect public ex-post equilibrium (PPXE), and show that it can be characterized with an extension of the techniques used to study perfect public equilibria. We develop identifiability conditions that are sufficient for a folk theorem; these conditions imply that there are PPXE in which the payoffs are approximately the same as if the monitoring structure and payoff functions were known. Finally, we define type-contingent PPXE, which allows players to condition their actions on their initial private information, and we provide its linear programming characterization.