Correlated Equilibria in Stochastic Games with Borel Measurable Payoffs

Abstract

An autonomous correlation device in a multistage game is a device that, before every stage, chooses for each player a private signal, possibly in a correlated way, and reveals to each player the signal chosen for him. The chosen signals depend only on previous signals, and not on the actions of the players. An extensive-form correlated \(\varepsilon \)-equilibrium in a multistage game is an \(\varepsilon \)-equilibrium in an extended game that includes an autonomous correlation device. In this paper we prove that every stochastic game with Borel measurable bounded payoffs has an extensive-form correlated \(\varepsilon \)-equilibrium, for every \(\varepsilon >0\).