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Non-zero-sum stopping games in discrete time

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  • Zhou Zhou

Abstract

We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game where players act simultaneously at each stage. We show that there exists a Nash equilibrium in mixed stopping strategies. In the second part, we assume that one player has to act first at each stage. In this case, we show the existence of a Nash equilibrium in pure stopping strategies.

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  • Zhou Zhou, 2015. "Non-zero-sum stopping games in discrete time," Papers 1508.06032, arXiv.org.
    • Handle: RePEc:arx:papers:1508.06032
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    References listed on IDEAS

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    1. Rida Laraki & Eilon Solan, 2002. "Stopping Games in Continuous Time," Discussion Papers 1354, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    3. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
    4. Erhan Bayraktar & Zhou Zhou, 2014. "On a Stopping Game in continuous time," Papers 1409.6773, arXiv.org, revised Jul 2015.
    5. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 1999. "Stopping Games with Randomized Strategies," Discussion Papers 1258, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Erhan Bayraktar & Zhou Zhou, 2014. "On Zero-sum Optimal Stopping Games," Papers 1408.3692, arXiv.org, revised Mar 2017.
    7. 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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