On the elimination of dominated strategies in stochastic models of evolution with large populations

• 成果类型: Article
• 署名作者: Kuzmics, Christoph
• 署名单位: Northwestern University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2010.10.002
• 发表日期: 2011
• 页码: 452-466
• 关键词: Learning; experimentation; S-infinity-procedure; Weak dominance; Iterated strict dominance

摘要

A stochastic myopic best-reply dynamics is said to have property (W), for a given number of players n, if every pure weakly dominated strategy in every n-player game is eliminated in the long-run distribution of play induced by the dynamics. In this paper I give a necessary and sufficient condition that a dynamics has to satisfy in order for it to have property (W). The key determinant is found to be the sensitivity of the learning-rate to small payoff differences, inherent in the dynamics. If this sensitivity is higher than a certain cut-off, which depends on the number of players, then the dynamics satisfies property (W). If it is equal to or below that cut-off, then the dynamics does not satisfy property (W). (C) 2010 Elsevier Inc. All rights reserved.