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Zero-sum stopping games with asymmetric information

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  • Gensbittel, Fabien
  • Grün, Christine

Abstract

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), where X is only observed by player 1 and Y only by player 2, implying that the players have access to stopping times with respect to different filtrations. We show the existence of a value in mixed stopping times and provide a variational characterization for the value as a function of the initial distribution of the Markov chains. We also prove a verification theorem for optimal stopping rules which allows to construct optimal stopping times. Finally we use our results to solve explicitly two generic examples.

Suggested Citation

  • Gensbittel, Fabien & Grün, Christine, 2017. "Zero-sum stopping games with asymmetric information," TSE Working Papers 17-859, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:32183
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    References listed on IDEAS

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    1. Bernard De Meyer, 1996. "Repeated Games, Duality and the Central Limit Theorem," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 237-251, February.
    2. Tiziano De Angelis & Fabien Gensbittel & St'ephane Villeneuve, 2017. "A Dynkin game on assets with incomplete information on the return," Papers 1705.07352, arXiv.org, revised May 2019.
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    6. Fabien Gensbittel, 2015. "Extensions of the Cav( u ) Theorem for Repeated Games with Incomplete Information on One Side," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 80-104, February.
    7. repec:dau:papers:123456789/6927 is not listed on IDEAS
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    11. Fabien Gensbittel & Catherine Rainer, 2018. "A Two-Player Zero-sum Game Where Only One Player Observes a Brownian Motion," Dynamic Games and Applications, Springer, vol. 8(2), pages 280-314, June.
    12. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2007. "Social Learning in One-Arm Bandit Problems," Econometrica, Econometric Society, vol. 75(6), pages 1591-1611, November.
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    14. Pierre Cardaliaguet & Catherine Rainer, 2012. "Games with Incomplete Information in Continuous Time and for Continuous Types," Dynamic Games and Applications, Springer, vol. 2(2), pages 206-227, June.
    15. 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.
    16. 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.
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    19. 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.
    20. De Meyer, Bernard, 2010. "Price dynamics on a stock market with asymmetric information," Games and Economic Behavior, Elsevier, vol. 69(1), pages 42-71, May.
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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. 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.
    3. Tiziano De Angelis & Erik Ekstrom & Kristoffer Glover, 2018. "Dynkin games with incomplete and asymmetric information," Papers 1810.07674, arXiv.org, revised Jul 2020.
    4. Tiziano De Angelis & Nikita Merkulov & Jan Palczewski, 2020. "On the value of non-Markovian Dynkin games with partial and asymmetric information," Papers 2007.10643, arXiv.org, revised Feb 2021.
    5. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    6. Tiziano De Angelis & Erik Ekstrom, 2019. "Playing with ghosts in a Dynkin game," Papers 1905.06564, arXiv.org.

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