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On a Markov Game with One-Sided Incomplete Information

Author

Listed:
  • Johannes Horner

    (Cowles Foundation, Yale University)

  • Dinah Rosenberg

    (Dept. of Economics and Decision Sciences, HEC Paris and GREGHEC)

  • Eilon Solan

    (School of Mathematical Sciences, Tel Aviv University)

  • Nicolas Vieille

    (Dept of Economics and Decision Sciences, HEC Paris and GREGHEC)

Abstract

We apply the average cost optimality equation to zero-sum Markov games, by considering a simple game with one-sided incomplete information that generalizes an example of Aumann and Maschler (1995). We determine the value and identify the optimal strategies for a range of parameters.

Suggested Citation

  • Johannes Horner & Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2009. "On a Markov Game with One-Sided Incomplete Information," Cowles Foundation Discussion Papers 1737, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1737
    as

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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d17/d1737.pdf
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    References listed on IDEAS

    as
    1. George J. Mailath & Larry Samuelson, 2001. "Who Wants a Good Reputation?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 415-441.
    2. Wiseman, Thomas, 2008. "Reputation and impermanent types," Games and Economic Behavior, Elsevier, vol. 62(1), pages 190-210, January.
    3. Jérôme Renault, 2006. "The Value of Markov Chain Games with Lack of Information on One Side," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 490-512, August.
    4. Phelan, Christopher, 2006. "Public trust and government betrayal," Journal of Economic Theory, Elsevier, vol. 130(1), pages 27-43, September.
    5. Abraham Neyman, 2008. "Existence of optimal strategies in Markov games with incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 581-596, December.
    6. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    7. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    8. Steve Alpern & Shmuel Gal, 2002. "Searching for an Agent Who May OR May Not Want to be Found," Operations Research, INFORMS, vol. 50(2), pages 311-323, April.
    9. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Repeated game with incomplete information; Zero-sum games; Partially observable Markov decision processes;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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