Repeated Games with Partial Monitoring: the Stochastic Signaling Case

In this work we extend a result of Lehrer characterizing the correlated equilibrium payoffs in undiscounted two player repeated games with partial monitoring to the case in which the signals are permitted to be stochastic. In particular we develop appropriate versions of Lehrer's concepts of ``indistinguishable'' and ``more informative.'' We also show that any payoff associated with a (correlated) distribution on strategy vectors in the stage game such that neither player can profitably deviate from one of his strategies to another that is indistinguishable and more informative is the payoff of a correlated equilibrium of the supergame.