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.