The refinement of Nash equilibrium based on equilibrium models of imperfectly rational behavior
Games and Economic Behavior · 2026 · Rodrigo A. Velez、Alexander L. Brown
中文摘要
本文引入一种纳什均衡 (NE) 的精炼, 用以判定被弱占优的 NE 在博弈中是否具有相关性。我们对 Harsanyi (1973) 提出的"可逼近性"概念加以改造——该概念最初建立在收益带有随机扰动的博弈之上——并将其扩展至一个更广泛的家族, 该家族涵盖了使用最广泛的不完全理性行为均衡模型。我们识别出一个唯一的 NE 精炼——近似收益单调均衡 (APME), 它与可由正则随机反应均衡以及控制成本模型逼近的 NE 集合恰好重合。我们主张采用 APME, 依据在于: 1) 它建立在能够为经验观察到的行为提供合理化解释的模型之上; 2) 它能够在不同均衡之间做出甄别, 而不会自动剔除被弱占优的行为; 3) 在 NE 结构已知的应用中, 它具有计算上的简便性。我们通过三个应用来说明 APME 的价值, 在这些应用中, 实证研究表明被弱占优的 NE 具有相关性。
Abstract
This paper introduces a refinement of Nash equilibrium (NE) to determine the relevance of weakly dominated NE in games. We adapt Harsanyi (1973)'s concept of “approachability,” originally based on games with randomly disturbed payoffs, and extend it to a broader family that encompasses the most widely used equilibrium models of imperfectly rational behavior. We identify a singular NE refinement, approximate payoff monotone equilibrium (APME), that coincides with the set of NE that are approachable by regular quantal response equilibria as well as control cost models. We advocate for APME based on its 1) foundation in models that rationalize empirically observed behavior; 2) ability to discriminate between equilibria without automatically discarding weakly dominated behavior; and 3) computational simplicity in applications where the structure of NE is known. We illustrate the value of APME in three applications in which empirical studies suggest that weakly dominated NE are relevant.