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Zero-Sum Stopping Games with Asymmetric Information

Author

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  • Fabien Gensbittel

    (Toulouse School of Economics, University of Toulouse Capitole, 31000 Toulouse, France)

  • Christine Grün

    (Toulouse School of Economics, University of Toulouse Capitole, 31000 Toulouse, France)

Abstract

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two independent continuous-time Markov chains, where the first Markov chain is only observed by player 1 and the second Markov chain is only observed 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

  • Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    • Handle: RePEc:inm:ormoor:v:44:y:2019:i:1:p:277-302
    DOI: 10.1287/moor.2017.0924
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    References listed on IDEAS

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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. Tiziano De Angelis & Erik Ekström & Kristoffer Glover, 2022. "Dynkin Games with Incomplete and Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 560-586, February.
    3. 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.
    4. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    5. 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.
    6. Tiziano De Angelis & Erik Ekstrom, 2019. "Playing with ghosts in a Dynkin game," Papers 1905.06564, arXiv.org.

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