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Markov Games with Frequent Actions and Incomplete Information

Author

Listed:
  • Cardaliaguet, Pierre
  • Rainer, Catherine
  • Rosenberg, Dinah
  • Vieille , Nicolas

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

  • Cardaliaguet, Pierre & Rainer, Catherine & Rosenberg, Dinah & Vieille , Nicolas, 2013. "Markov Games with Frequent Actions and Incomplete Information," HEC Research Papers Series 1007, HEC Paris.
    • Handle: RePEc:ebg:heccah:1007
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    Cited by:

    1. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Staudigl, Mathias & Steg, Jan-Henrik, 2014. "On Repeated Games with Imperfect Public Monitoring: From Discrete to Continuous Time," Center for Mathematical Economics Working Papers 525, Center for Mathematical Economics, Bielefeld University.
    3. Fabien Gensbittel & Jérôme Renault, 2015. "The Value of Markov Chain Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 820-841, October.

    More about this item

    Keywords

    stochastic; zero sum; Markov chain; Hamilton-Jacobi equation; incomplete information;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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