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Existence of Optimal Strategies in Markov Games with Incomplete Information

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  • Abraham Neyman

Abstract

The existence of a value and optimal strategies is proved for the class of twoperson repeated games where the state follows a Markov chain independently of players’ actions and at the beginning of each stage only player one is informed about the state. The results apply to the case of standard signaling where players’ stage actions are observable, as well as to the model with general signals provided that player one has a nonrevealing repeated game strategy. The proofs reduce the analysis of these repeated games to that of classical repeated games with incomplete information on one side.

Suggested Citation

  • Abraham Neyman, 2005. "Existence of Optimal Strategies in Markov Games with Incomplete Information," Discussion Paper Series dp413, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp413
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    References listed on IDEAS

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    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
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    Cited by:

    1. Fabien Gensbittel, 2019. "Continuous-Time Markov Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 9(3), pages 671-699, September.
    2. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. 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.
    4. Johannes Hörner & Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2010. "On a Markov Game with One-Sided Information," Operations Research, INFORMS, vol. 58(4-part-2), pages 1107-1115, August.
    5. 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.
    6. 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.
    7. Jérôme Renault & Xavier Venel, 2017. "Long-Term Values in Markov Decision Processes and Repeated Games, and a New Distance for Probability Spaces," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 349-376, May.
    8. 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.
    9. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    10. 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.
    11. Johannes Hörner & Satoru Takahashi & Nicolas Vieille, 2015. "Truthful Equilibria in Dynamic Bayesian Games," Econometrica, Econometric Society, vol. 83(5), pages 1795-1848, September.
    12. Jérôme Renault, 2012. "The Value of Repeated Games with an Informed Controller," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 154-179, February.
    13. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 172-207, March.
    14. Bruno Ziliotto, 2016. "A Tauberian Theorem for Nonexpansive Operators and Applications to Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1522-1534, November.

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