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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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