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Playing with ghosts in a Dynkin game

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  • De Angelis, Tiziano
  • Ekström, Erik

Abstract

We study a class of two-player optimal stopping games (Dynkin games) of preemption type, with uncertainty about the existence of competitors. The set-up is well-suited to model, for example, real options in the context of investors who do not want to publicly reveal their interest in a certain business opportunity. We show that if the underlying process is a Rd-valued, continuous, strong Markov process, and the stopping payoff is a continuous function (with mild integrability properties) there exists a Nash equilibrium in randomised stopping times for the game. Moreover, the equilibrium strategies and the expected payoffs of the two players are computed explicitly in terms of the corresponding one-player game. To the best of our knowledge this is the first paper to address this version of Dynkin games.

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  • De Angelis, Tiziano & Ekström, Erik, 2020. "Playing with ghosts in a Dynkin game," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6133-6156.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:6133-6156
    DOI: 10.1016/j.spa.2020.05.005
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    5. Lambrecht, Bart & Perraudin, William, 2003. "Real options and preemption under incomplete information," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 619-643, February.
    6. 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).
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    Cited by:

    1. Bodnariu, Andi & Lindensjö, Kristoffer, 2024. "A controller-stopper-game with hidden controller type," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    2. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.

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