Multiplicity of Equilibria in the War of Attrition with Two-Sided Asymmetric Information
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| Format: | Preprint |
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2026
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| _version_ | 1866910052764352512 |
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| author | Castillo-Quintana, Martin Miranda-Romero, Gianfranco |
| author_facet | Castillo-Quintana, Martin Miranda-Romero, Gianfranco |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_13634 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiplicity of Equilibria in the War of Attrition with Two-Sided Asymmetric Information Castillo-Quintana, Martin Miranda-Romero, Gianfranco Theoretical Economics 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. |
| title | Multiplicity of Equilibria in the War of Attrition with Two-Sided Asymmetric Information |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2603.13634 |