Type-Contingent Perfect Public Ex-Post Equilibria∗

We consider repeated games with incomplete information where players observe imperfect public signals of the actions and the map from actions to signal distributions is itself unknown. To do so, we introduce the concept of type-contingent perfect public ex-post equilibrium or T-PPXE, which reduces to the PPXE of Fudenberg and Yamamoto (2009) in complete-information games, and reduces to the belief-free equilibrium of Hörner and Lovo (2009) when actions are perfectly observed. We provide a sufficient condition for the folk theorem, and a characterization of the T-PPXE payoffs in games with a known monitoring structure. Under a “sufficient rank” condition, we show that the theorems of Hörner and Lovo (2009) on games with perfectly observed actions extend to imperfect monitoring, and that the folk theorem holds if each pair of states can be distinguished by the private information of at least three players. Journal of Economic Literature Classification Numbers: C72, C73.