Rationality and Extensive Form Correlated Equilibria in Stochastic Games

We define the notion of rational payoffs in stochastic games. We then prove that the set of rational payoffs coincides with the set of extensive form correlated equilibrium payoffs; those are equilibrium payoffs in an extended game that includes an autonomous correlation device: a device that sends at every stage a private signal to each player, which is independent of the play, but may depend on previous signals. In particular, it follows that communication between the players and/or between the players and the correlation device cannot increase the set of equilibrium payoffs. ∗This is a thorough revision of “Extensive Form Correlated Equilibria”, discussion paper #175 , Center for Rationality and Interactive Decision Theory, The Hebrew University of Jerusalem. †Department of Managerial Economics and Decision Sciences, Kellogg Graduate School of Management, Northwestern University, 2001 Sheridan Road, Evanston IL 60208. e-mail: [email protected] ‡I thank Rakesh Vohra, the associate editor of the International Journal of Game Theory and two anonymous referees for their helpful comments.