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Stochastic Games with a Single Controller and Incomplete Information

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  • Dinah Rosenberg
  • Eilon Solan
  • Nicolas Vieille

Abstract

We study stochastic games with incomplete information on one side, where the transition is controlled by one of the players. We prove that if the informed player also controls the transition, the game has a value, whereas if the uninformed player controls the transition, the max-min value, as well as the min-max value, exist, but they may differ. We discuss extensions to the case of incomplete information on both sides.
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Suggested Citation

  • Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Stochastic Games with a Single Controller and Incomplete Information," Discussion Papers 1346, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1346
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    References listed on IDEAS

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    6. repec:dau:papers:123456789/6231 is not listed on IDEAS
    7. Nicolas Vieille & Dinah Rosenberg, 2000. "The Maxmin of Recursive Games with Incomplete Information on one Side," Post-Print hal-00481429, HAL.
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    16. Dinah Rosenberg & Nicolas Vieille, 2000. "The Maxmin of Recursive Games with Incomplete Information on one Side," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 23-35, February.
    17. Bernard de Meyer, 1996. "Repeated games, Duality, and the Central Limit Theorem," Post-Print hal-00259714, HAL.
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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. Hugo Gimbert & Jérôme Renault & Sylvain Sorin & Xavier Venel & Wieslaw Zielonka, 2016. "On the values of repeated games with signals," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01006951, HAL.
    3. P. Cardaliaguet, 2008. "Representations Formulas for Some Differential Games with Asymmetric Information," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 1-16, July.
    4. 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.
    5. 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.
    6. 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.
    7. Banas, Lubomir & Ferrari, Giorgio & Randrianasolo, Tsiry Avisoa, 2020. "Numerical Appromixation of the Value of a Stochastic Differential Game with Asymmetric Information," Center for Mathematical Economics Working Papers 630, Center for Mathematical Economics, Bielefeld University.
    8. Dhruva Kartik & Ashutosh Nayyar, 2021. "Upper and Lower Values in Zero-Sum Stochastic Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 11(2), pages 363-388, June.
    9. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Stochastic Games with Imperfect Monitoring," Discussion Papers 1341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Xiaoxi Li & Xavier Venel, 2016. "Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "," Post-Print hal-01302553, HAL.
    11. Xiaoxi Li & Xavier Venel, 2016. "Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01302553, HAL.
    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. Xiaoxi Li & Xavier Venel, 2016. "Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "," PSE-Ecole d'économie de Paris (Postprint) hal-01302553, HAL.
    14. 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.
    15. Erim Kardeş & Fernando Ordóñez & Randolph W. Hall, 2011. "Discounted Robust Stochastic Games and an Application to Queueing Control," Operations Research, INFORMS, vol. 59(2), pages 365-382, April.
    16. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series dp295, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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    JEL classification:

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

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