Correlated Equilibrium, Public Signalling and Absorbing Games

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 > 0 there exists a probability distribution p over the space of pure strategy profiles such that if a pure strategy profile is chosen according to p and each player is informed of his pure strategy, no player can profit more than in any sufficiently long game by deviating from the recommended strategy. ∗Department of Managerial Economics and Decision Sciences, Kellogg Graduate School of Management, Northwestern University, 2001 Sheridan Road, Evanston IL 60208. e-mail: [email protected] †Department of Managerial Economics and Decision Sciences, Kellogg Graduate School of Management, Northwestern University, 2001 Sheridan Road, Evanston IL 60208. e-mail: [email protected]