We study the perfect type-contingently public ex-post equilibrium (PTXE) of 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. The PTXE payoffs when players are patient are determined by the intersection of the maximal half spaces in various directions; we focus on the “cross-state” directions that consider payoffs in two or more states. We develop conditions under which the maximal half spaces in these directions impose no constraints on the equilibrium set, so that equilibrium play can be as if the players have learned the state. We use these conditions to provide a sufficient condition for the folk theorem, and a characterization of the PTXE payoffs in games with a known monitoring structure.
['Drew Fudenberg', 'Yuichi Yamamoto']
Learning from Private Information in Noisy Repeated Games