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Solving two-state Markov games with incomplete information on one side

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  • Ashkenazi-Golan, Galit
  • Rainer, Catherine
  • Solan, Eilon

Abstract

We study the optimal use of information in Markov games with incomplete information on one side and two states. We provide a finite-stage algorithm for calculating the limit value as the gap between stages goes to 0, and an optimal strategy for the informed player in the limiting game in continuous time. This limiting strategy induces an ϵ-optimal strategy for the informed player, provided the gap between stages is small. Our results demonstrate when the informed player should use her information and how.

Suggested Citation

  • Ashkenazi-Golan, Galit & Rainer, Catherine & Solan, Eilon, 2020. "Solving two-state Markov games with incomplete information on one side," Games and Economic Behavior, Elsevier, vol. 122(C), pages 83-104.
    • Handle: RePEc:eee:gamebe:v:122:y:2020:i:c:p:83-104
    DOI: 10.1016/j.geb.2020.04.004
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    References listed on IDEAS

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    1. Fabien Gensbittel, 2019. "Continuous-Time Markov Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 9(3), pages 671-699, September.
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    7. Pierre Cardaliaguet & Catherine Rainer & Dinah Rosenberg & Nicolas Vieille, 2016. "Markov Games with Frequent Actions and Incomplete Information—The Limit Case," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 49-71, February.
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    Cited by:

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    2. Chen, Fang & Guo, Xianping, 2023. "Two-person zero-sum risk-sensitive stochastic games with incomplete reward information on one side," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 218-245.
    3. Ashkenazi-Golan, Galit & Hernández, Penélope & Neeman, Zvika & Solan, Eilon, 2023. "Markovian persuasion with two states," LSE Research Online Documents on Economics 119970, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    Repeated games with incomplete information on one side; Markov games; Value; Optimal strategy; Algorithm;
    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
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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