Correlated equilibria of two person repeated games with random signals

In this work we extend a result of Lehrer (Math Oper Res 17(1):175-199, 1992a) characterising 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 individually rational payoff associated with a (correlated) distribution on pure action profiles in the stage game such that neither player can profitably deviate from one of his actions to another that is indistinguishable and more informative is the payoff of a correlated equilibrium of the infinitely repeated game.