博弈论中 attrition 战争的均衡多重性
Multiplicity of Equilibria in the War of Attrition with Two-Sided Asymmetric Information
AI总结：
本文研究了双面不对称信息下的 attrition 战争模型，分析了均衡多重性的来源，指出类型分布的条件决定了均衡形式，并证明了两种不同精炼方法在有限类型支持时等价，可选唯一均衡。
摘要：
在政治经济学中，具有双面不对称信息的 attrition 战争是一个基础模型，但通常允许连续的完美贝叶斯均衡。本文刻画了均衡多重性的来源。我们识别出类型分布的条件，决定了哪种多重性出现：当危险潜力下限——危险率积分归一化后的积分发散时，自由参数是策略的相对攻击性；当该极限有限时，自由参数是立即投降类型的质量。我们证明了 Amann-Leininger 收益扰动和引入行为类型——两种看似不同的精炼——在数学上等价，并且在类型支持有限时，能够选择唯一均衡。对于无界支持，多重性仍然存在。这些结果为应用理论家提供了指导：选择具有有限支持的分布确保现有精炼方法提供唯一预测。
英文摘要：
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.
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