Characterization of Correlated Equilibria in Stochastic Games

Eilon Solan

International Journal of Game Theory 30 (2001), 259-277.

A general communication device is a device that at every stage of the game receives a private message from each player, and in return sends a private signal to each player; the signals the device sends depend on past play, past signals it sent, and past messages it received.

An autonomous correlation device is a general communication device where signals depend only on past signals the device sent, but not on past play or past messages it received.

We show that the set of all equilibrium payoffs in extended games that include a general communication device coincides with the set of all equilibrium payoffs in extended games

that include an autonomous correlation device. A stronger result is obtained when the punishment level is independent of the history.

The results hold in a most general setup: the state and action spaces are general, and the payoff function may be an arbitrary measurable function defined over the space of plays.