Markov Games with Frequent Actions and Incomplete Information

Pierre Cardaliaguet (), Catherine Rainer (), Dinah Rosenberg and Nicolas Vieille ()
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Pierre Cardaliaguet: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Catherine Rainer: LM - Laboratoire de mathématiques de Brest - UBO - Université de Brest - IBNM - Institut Brestois du Numérique et des Mathématiques - UBO - Université de Brest - CNRS - Centre National de la Recherche Scientifique
Dinah Rosenberg: GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique
Nicolas Vieille: GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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.

Date: 2016
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Published in Mathematics of Operations Research, 2016, 41 (1), pp.49-71. ⟨10.2139/ssrn.2344780⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02058235

DOI: 10.2139/ssrn.2344780

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