Correlated Equilibrium Payoffs and Public Signalling in Absorbing Games
Eilon Solan and Rakesh Vohra
International Journal of Game Theory, to appear.
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 e > 0 there exists a probability distribution p(e) 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 p(e) and each player is informed of his pure strategy, no player can profit more than e in any sufficiently long game by deviating from the recommended strategy.