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Symmetric Equilibria in Stochastic Timing Games

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  • Jan-Henrik Steg

Abstract

We construct subgame-perfect equilibria with mixed strategies for symmetric stochastic timing games with arbitrary strategic incentives. The strategies are qualitatively different for local first- or second-mover advantages, which we analyse in turn. When there is a local second-mover advantage, the players may conduct a war of attrition with stopping rates that we characterize in terms of the Snell envelope from the theory of optimal stopping. This is a very general result, but it provides a clear interpretation. When there is a local first-mover advantage, stopping typically results from preemption and is abrupt. Equilibria may differ in the degree of preemption, precisely when it is triggered or not. We develop an algorithm to characterize when preemption is inevitable and to construct corresponding payoff-maximal symmetric equilibria.

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  • Jan-Henrik Steg, 2015. "Symmetric Equilibria in Stochastic Timing Games," Papers 1507.04797, arXiv.org, revised May 2018.
    • Handle: RePEc:arx:papers:1507.04797
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    Cited by:

    1. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2015. "On the timing of innovation and imitation," MPRA Paper 69161, University Library of Munich, Germany.
    2. Georgiadis, George & Kim, Youngsoo & Kwon, H. Dharma, 2022. "The absence of attrition in a war of attrition under complete information," Games and Economic Behavior, Elsevier, vol. 131(C), pages 171-185.
    3. George Georgiadis & Youngsoo Kim & H. Dharma Kwon, 2021. "The Absence of Attrition in a War of Attrition under Complete Information," Papers 2110.12013, arXiv.org, revised Nov 2021.
    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. Décamps, Jean-Paul & Gensbittel, Fabien & Mariotti, Thomas, 2022. "Mixed-Strategy Equilibria in the War of Attrition under Uncertainty," TSE Working Papers 22-1374, Toulouse School of Economics (TSE), revised 22 Nov 2023.
    6. Steg, Jan-Henrik & Thijssen, Jacco J.J., 2023. "Strategic investment with positive externalities," Games and Economic Behavior, Elsevier, vol. 138(C), pages 1-21.
    7. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    8. H. Dharma Kwon, 2019. "Game of Variable Contributions to the Common Good under Uncertainty," Papers 1904.00500, arXiv.org.
    9. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2016. "When should a winner take all, or pay some? Innovation and imitation incentives in a dynamic duopoly," MPRA Paper 75465, University Library of Munich, Germany.

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