Nash and publicly correlated equilibrium payoffs in non zero sum differential games using mixed strategies

Anne Souquière (1, 2)

1 LM - Laboratoire de mathématiques de Brest
2 LUSSI - Département Logique des Usages, Sciences sociales et Sciences de l'Information

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 on pure strategies. We prove that the set of Nash equilibrium payoffs when using mixed strategies is convex and compact. Unexpectedly, this set is larger than the closed convex hull of the set of Nash equilibrium payoffs using pure strategies. We give a characterization for the Nash equilibrium payoffs using mixed strategies as reachable and consistent, these concepts being adapted to random controls. Finally, still referring to repeated games, 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.

Mots clés: Differential games; Nash equilibrium; correlated equilibrium

Domaines: Optimisation et contrôle [math.OC]

Anne Souquière. Nash and publicly correlated equilibrium payoffs in non zero sum differential games using mixed strategies. 2009. ⟨hal-00418629⟩