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Markov Games with Frequent Actions and Incomplete Information

Author

Listed:
  • 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)

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.

Suggested Citation

  • Pierre Cardaliaguet & Catherine Rainer & Dinah Rosenberg & Nicolas Vieille, 2016. "Markov Games with Frequent Actions and Incomplete Information," Post-Print hal-02058235, HAL.
  • Handle: RePEc:hal:journl:hal-02058235
    DOI: 10.2139/ssrn.2344780
    as

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