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 payo¤ at every future stage. We prove that every multi-player absorbing game admits a correlated equilibrium payo¤. In other words, for every e > 0 there exists a probability distribution pe over the space of pure strategy profiles that satisfies the following. With probability at least 1 e, if a pure strategy profile is chosen according to pe and each player is informed of his pure strategy, no player can profit more than e in any su‰ciently long game by deviating from the recommended strategy.