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.