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The absence of attrition in a war of attrition under complete information

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  • Georgiadis, George
  • Kim, Youngsoo
  • Kwon, H. Dharma

Abstract

We consider a two-player game of war of attrition under complete information. It is well-known that this class of games admits equilibria in pure, as well as mixed strategies, and much of the literature has focused on the latter. We show that if the players' payoffs whilst in “war” vary stochastically and their exit payoffs are heterogeneous, then the game admits Markov Perfect equilibria in pure strategies only. This is true irrespective of the degree of randomness and heterogeneity, thus highlighting the fragility of mixed-strategy equilibria to a natural perturbation of the canonical model. In contrast, when the players' flow payoffs are deterministic or their exit payoffs are homogeneous, the game admits equilibria in pure and mixed strategies.

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  • 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.
    • Handle: RePEc:eee:gamebe:v:131:y:2022:i:c:p:171-185
    DOI: 10.1016/j.geb.2021.11.004
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    Cited by:

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    2. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    3. Steg, Jan-Henrik & Thijssen, Jacco J.J., 2023. "Strategic investment with positive externalities," Games and Economic Behavior, Elsevier, vol. 138(C), pages 1-21.
    4. Décamps, Jean-Paul & Gensbittel, Fabien & Mariotti, Thomas, 2022. "The War of Attrition under Uncertainty: Theory and Robust Testable Implications," TSE Working Papers 22-1374, Toulouse School of Economics (TSE), revised Jun 2024.
    5. Betto, Maria & Thomas, Matthew W., 2024. "Asymmetric all-pay auctions with spillovers," Theoretical Economics, Econometric Society, vol. 19(1), January.

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