Nash Equilibrium Payoffs in Mixed Strategies

Abstract

We consider non zero sum two players differential games. We study Nash equilibrium payoffs and publicly correlated equilibrium payoffs. If players use deterministic strategies, it has been proved that the Nash equilibrium payoffs are precisely the reachable and consistent payoffs. Referring to repeated games, we introduce mixed strategies which are probability distributions over pure strategies. We give a characterization of the set of Nash equilibrium payoffs in mixed strategies. Unexpectedly, this set is larger than the closed convex hull of the set of Nash equilibrium payoffs in pure strategies. Finally, we study the set of publicly correlated equilibrium payoffs for differential games and show that it is the same as the set of Nash equilibrium payoffs using mixed strategies.KeywordsNon cooperative differential gamesNash equilibrium payoffPublicly correlated equilibrium payoffMixed strategy