Fast convergence in evolutionary models: A. Lyapunov approach

• 成果类型: Article
• 署名作者: Ellison, Glenn; Fudenberg, Drew; Imhof, Lorens A.
• 署名单位: Massachusetts Institute of Technology (MIT); Harvard University; University of Bonn
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2015.10.008
• 发表日期: 2016
• 页码: 1-36
• 关键词: Hitting time; Learning model; Local interaction; Lyapunov function; Markov chain; Recency

摘要

Evolutionary models in which N players are repeatedly matched to play a game have fast convergence to a set A if the models both reach A quickly and leave A slowly, where quickly and slowly refer to whether the expected hitting and exit times remain bounded when N tends to infinity. We provide simple and general Lyapunov criteria which are sufficient for reaching quickly and leaving slowly. We use these criteria to determine aspects of learning models that promote fast convergence. (C) 2015 Elsevier Inc. All rights reserved.