Correlated equilibrium payoffs and public signalling in absorbing games

An absorbing game is a repeated game where some 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 multi-player absorbing game admits a correlated equilibrium payoff. In other words, for every epsilon > 0 there exists a probability distribution p(epsilon) over the space of pure strategy profiles that satisfies the following. With probability at least 1 - epsilon, if a pure strategy profile is chosen according to p(epsilon) 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.