Correlated Equilibria in Nonzero-Sum Differential Games

Abstract

This paper is our second study of correlated equilibria in nonzero-sum differential games of prescribed duration. Our first work, based on relaxed controls of the players, dealt with linear differential games. In this paper, we use mixed correlated strategies with finite supports and consider nonzero-sum differential games with the open-loop information pattern, for which no equilibrium solution has been known to exist so far. Assuming very mild conditions about the primitive data (dynamical systems, payoff functionals), we prove that all games under consideration possess correlated ϵ-equilibria for any ϵ > 0. For linear differential games one can use such ϵ-equilibria to construct chattering ϵ-equilibrium solutions in the class of relaxed correlated strategies of the players. Our main result also implies Wilson′s minimax theorem for zero-sum differential games with no information.