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 gamed terminates, and the players receive some terminal payoff at every future state. We prove that every multi-player absorbing game admits a correlated equilibrium payoff. In other words, for every ϵ > 0 there exists a probability distribution pϵ over the space of pure strategy profiles that satisfies the following. With probability at least 1 − ϵ, if a pure strategy profile is chosen according to pϵ and each player is informed of his pure strategy, no player can profit more than ϵ in any sufficiently long game by deviating from the recommended strategy.