Correlated Equilibrium, Public Signaling and Absorbing Games

Abstract

An absorbing game is a repeated game where some of the action combinations are absorbing, in the sense that whenever they are played, there is a positive probability that the game terminates, and the players receive some terminal payoff at every future stage. We prove that every n-player absorbing game admits a correlated equilibrium. In other words, for every epsilon>0 there exits a probability distribution p (epsilon subscript) over the space of pure strategy profiles such that if a pure strategy profile is chosen according to p (epsilon subscript) and each player is informed of his pure strategy, no player can profit more than epsilon in any sufficiently long game by deviating from the recommended strategy.