A characterization of quasi-perfect equilibria

• 成果类型: Article
• 署名作者: Gatti, Nicola; Gilli, Mario; Marchesi, Alberto
• 署名单位: Polytechnic University of Milan; University of Milano-Bicocca
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2020.04.012
• 发表日期: 2020
• 页码: 240-255
• 关键词: Quasi-perfect equilibrium; characterization; Trembles; Games in sequence form

摘要

We provide a characterization of quasi perfect equilibria in n-player games, showing that any quasi-perfect equilibrium can be obtained as limit point of a sequence of Nash equilibria of a certain class of perturbed games in sequence form, and any limit point of a sequence of Nash equilibria of these perturbed games is a quasi-perfect equilibrium. We prove that, in games with three or more players, we need trembles defined as rational functions of the perturbation magnitude epsilon, whereas, in two-player games with nature, trembles expressed in terms of polynomial functions of epsilon suffice. Exploiting the relationship between sequence form and extensive form, we also provide a similar characterization in terms of perturbed games in extensive form, though not compliant with Selten's definition of perturbed game. (C) 2020 Elsevier Inc. All rights reserved.