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Dynamical Analysis of a Repeated Game with Incomplete Information

Author

Listed:
  • Xavier Bressaud

    (Université Paul Sabatier, Institut de Mathématiques de Toulouse, F-31062 Toulouse Cedex, France)

  • Anthony Quas

    (Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 2Y2)

Abstract

We study a two player repeated zero-sum game with asymmetric information introduced by Renault in which the underlying state of the game undergoes Markov evolution (parameterized by a transition probability, p , in the range 1 2 to 1). Hörner, Rosenberg, Solan and Vieille identified an optimal strategy, σ * for the informed player for p in the range [ 1 2 , 2 3 ] . We extend the range on which σ * is proved to be optimal to about [ 1 2 , 0.719 ] and prove that it fails to be optimal at a value around 0.7328. Our techniques make use of tools from dynamical systems, specifically the notion of pressure, introduced by D. Ruelle.

Suggested Citation

  • Xavier Bressaud & Anthony Quas, 2017. "Dynamical Analysis of a Repeated Game with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1085-1105, November.
    • Handle: RePEc:inm:ormoor:v:42:y:2017:i:4:p:1085-1105
    DOI: 10.1287/moor.2016.0839
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    References listed on IDEAS

    as
    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    repeated game; optimal strategy;

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