Markov games with frequent actions and incomplete information

Pierre Cardaliaguet (1) , Catherine Rainer (2) , Dinah Rosenberg (3) , Nicolas Vieille (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LM - Laboratoire de mathématiques de Brest
3 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC

We study a two-player, zero-sum, stochastic game with incomplete information on one side in which the players are allowed to play more and more frequently. The informed player observes the realization of a Markov chain on which the payoffs depend, while the non-informed player only observes his opponent's actions. We show the existence of a limit value as the time span between two consecutive stages vanishes; this value is characterized through an auxiliary optimization problem and as the solution of an Hamilton-Jacobi equation.

Mots clés: Markov games; incomplete information; zero-sum games; Hamilton-Jacobi equations; repeated games

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet, Catherine Rainer, Dinah Rosenberg, Nicolas Vieille. Markov games with frequent actions and incomplete information. 2013. ⟨hal-00843475⟩