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Dynkin games with incomplete and asymmetric information

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  • Tiziano De Angelis
  • Erik Ekstrom
  • Kristoffer Glover

Abstract

We study the value and the optimal strategies for a two-player zero-sum optimal stopping game with incomplete and asymmetric information. In our Bayesian set-up, the drift of the underlying diffusion process is unknown to one player (incomplete information feature), but known to the other one (asymmetric information feature). We formulate the problem and reduce it to a fully Markovian setup where the uninformed player optimises over stopping times and the informed one uses randomised stopping times in order to hide their informational advantage. Then we provide a general verification result which allows us to find the value of the game and players' optimal strategies by solving suitable quasi-variational inequalities with some non-standard constraints. Finally, we study an example with linear payoffs, in which an explicit solution of the corresponding quasi-variational inequalities can be obtained.

Suggested Citation

  • Tiziano De Angelis & Erik Ekstrom & Kristoffer Glover, 2018. "Dynkin games with incomplete and asymmetric information," Papers 1810.07674, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:1810.07674
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    References listed on IDEAS

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    1. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    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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    16. Tiziano De Angelis & Fabien Gensbittel & Stephane Villeneuve, 2021. "A Dynkin Game on Assets with Incomplete Information on the Return," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 28-60, February.
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    19. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
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    Cited by:

    1. 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.
    2. Tiziano De Angelis & Jan Palczewski & Jacob Smith, 2025. "Martingale theory for Dynkin games with asymmetric information," Papers 2510.15616, arXiv.org.
    3. H. Dharma Kwon & Jan Palczewski, 2025. "Exit Game with Private Information," Mathematics of Operations Research, INFORMS, vol. 50(4), pages 2433-2469, November.
    4. Jacobovic, Royi & Levy, Yehuda John & Solan, Eilon, 2026. "Bayesian games with nested information," Theoretical Economics, Econometric Society, vol. 21(1), January.
    5. David Hobson & Gechun Liang & Edward Wang, 2021. "Callable convertible bonds under liquidity constraints and hybrid priorities," Papers 2111.02554, arXiv.org, revised Oct 2024.
    6. Starkov, Egor, 2023. "Only time will tell: Credible dynamic signaling," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    7. Banas, Lubomir & Ferrari, Giorgio & Randrianasolo, Tsiry Avisoa, 2025. "Numerical approximation of Dynkin games with asymmetric information," Center for Mathematical Economics Working Papers 733, Center for Mathematical Economics, Bielefeld University.
    8. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    9. Tiziano De Angelis & Erik Ekstrom, 2019. "Playing with ghosts in a Dynkin game," Papers 1905.06564, arXiv.org.
    10. Søren Johansen & Anders Ryghn Swensen, 2021. "Adjustment coefficients and exact rational expectations in cointegrated vector autoregressive models," CREATES Research Papers 2021-10, Department of Economics and Business Economics, Aarhus University.

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