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Dynkin games with heterogeneous beliefs

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Abstract

We study zero-sum optimal stopping games (Dynkin games) between two players who disagree about the underlying model. In a Markovian setting, a verification result is established showing that if a pair of functions can be found that satisfies some natural conditions then a Nash equilibrium of stopping times is obtained, with the given functions as the corresponding value functions. In general, however, there is no uniqueness of Nash equilibria, and different equilibria give rise to different value functions. As an example, we provide a thorough study of the game version of the American call option under heterogeneous beliefs. Finally, we also study equilibria in randomized stopping times.

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  • Marta Leniec & Kristoffer Glover & Erik Ekström, 2017. "Dynkin games with heterogeneous beliefs," Published Paper Series 2017-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    • Handle: RePEc:uts:ppaper:2017-2
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    File URL: https://www.cambridge.org/core/journals/journal-of-applied-probability/article/dynkin-games-with-heterogeneous-beliefs/BFFFA20FF978F1F4A2EDADE1BD8751BF
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    Cited by:

    1. Wong, Tat Wing & Fung, Ka Wai Terence & Leung, Kwai Sun, 2020. "Strategic bank closure and deposit insurance valuation," European Journal of Operational Research, Elsevier, vol. 285(1), pages 96-105.
    2. Tiziano De Angelis & Erik Ekstrom & Kristoffer Glover, 2018. "Dynkin games with incomplete and asymmetric information," Papers 1810.07674, arXiv.org, revised Jul 2020.
    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. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    5. Gunter H Meyer, 2016. "A PDE View of Games Options," Research Paper Series 369, Quantitative Finance Research Centre, University of Technology, Sydney.

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    Keywords

    Dynkin game; heterogeneous belief; multiple Nash equilibria; optimal stopping theory;
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