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Nash equilibria of threshold type for two-player nonzero-sum games of stopping

Author

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  • de Angelis, Tiziano

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Moriarty, John

    (Center for Mathematical Economics, Bielefeld University)

Abstract

This paper analyses two-player nonzero-sum games of optimal stopping on a class of regular diffusions with singular boundary behaviour (in the sense of Itô and McKean (1974) [19], p. 108). We prove that Nash equilibria are realised by stopping the diffusion at the first exit time from suitable intervals whose boundaries solve a system of algebraic equations. Under mild additional assumptions we also prove uniqueness of the equilibrium.

Suggested Citation

  • de Angelis, Tiziano & Ferrari, Giorgio & Moriarty, John, 2016. "Nash equilibria of threshold type for two-player nonzero-sum games of stopping," Center for Mathematical Economics Working Papers 563, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:563
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    File URL: https://pub.uni-bielefeld.de/download/2904748/2904761
    File Function: First Version, 2016
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    References listed on IDEAS

    as
    1. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    2. Rida Laraki & Eilon Solan, 2002. "Stopping Games in Continuous Time," Discussion Papers 1354, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Tim Leung & Xin Li, 2015. "Optimal Mean Reversion Trading With Transaction Costs And Stop-Loss Exit," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    4. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    5. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    6. Said Hamadène & Mohammed Hassani, 2014. "The multi-player nonzero-sum Dynkin game in discrete time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 179-194, April.
    7. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
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    More about this item

    Keywords

    nonzero-sum Dynkin games; Nash equilibrium; smooth-fit principle; regular diffusions; free boundary problems;

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