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Multiplicity of Equilibria in the War of Attrition with Two-Sided Asymmetric Information

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  • Martin Castillo-Quintana
  • Gianfranco Miranda-Romero

Abstract

The war of attrition with two-sided asymmetric information is a foundational model in political economy, yet it generically admits a continuum of perfect Bayesian equilibria. This paper characterizes the sources of equilibrium multiplicity. We identify conditions on the type distribution that determine which form of multiplicity arises: when the lower limit of the hazard potential -- the integral of the hazard rate normalized by type -- diverges, the free parameter is the relative aggressiveness of strategies; when that limit is finite, the free parameter is the mass of types conceding immediately. We prove that the Amann-Leininger payoff perturbation and the introduction of behavioral types -- two seemingly distinct refinements -- are mathematically equivalent and succeed in selecting a unique equilibrium if and only if the type support is bounded. For unbounded supports, multiplicity persists. These results provide guidance for applied theorists: choosing distributions with bounded support ensures existing refinements deliver unique predictions.

Suggested Citation

  • Martin Castillo-Quintana & Gianfranco Miranda-Romero, 2026. "Multiplicity of Equilibria in the War of Attrition with Two-Sided Asymmetric Information," Papers 2603.13634, arXiv.org.
    • Handle: RePEc:arx:papers:2603.13634
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    References listed on IDEAS

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    1. Hendricks, Ken & Weiss, Andrew & Wilson, Charles A, 1988. "The War of Attrition in Continuous Time with Complete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 663-680, November.
    2. Alexander Wolitzky, 2012. "Reputational Bargaining With Minimal Knowledge of Rationality," Econometrica, Econometric Society, vol. 80(5), pages 2047-2087, September.
    3. Catherine Hafer, 2006. "On the Origins of Property Rights: Conflict and Productionin the State of Nature," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(1), pages 119-143.
    4. Jack Fanning, 2016. "Reputational Bargaining and Deadlines," Econometrica, Econometric Society, vol. 84, pages 1131-1179, May.
    5. Myatt, David P., 2025. "The impact of perceived strength in the war of attrition," Games and Economic Behavior, Elsevier, vol. 150(C), pages 260-277.
    6. Fudenberg, Drew & Tirole, Jean, 1986. "A Theory of Exit in Duopoly," Econometrica, Econometric Society, vol. 54(4), pages 943-960, July.
    7. Kambe, Shinsuke, 1999. "Bargaining with Imperfect Commitment," Games and Economic Behavior, Elsevier, vol. 28(2), pages 217-237, August.
    8. Dilip Abreu & Faruk Gul, 2000. "Bargaining and Reputation," Econometrica, Econometric Society, vol. 68(1), pages 85-118, January.
    9. Roger B. Myerson, 2023. "Game Theory and the First World War," Journal of Economic Literature, American Economic Association, vol. 61(2), pages 716-735, June.
    10. Powell, Robert, 2017. "Taking Sides in Wars of Attrition," American Political Science Review, Cambridge University Press, vol. 111(2), pages 219-236, May.
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