Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics

• 成果类型: Article
• 署名作者: Hommes, Cars H.; Ochea, Marius I.
• 署名单位: University of Amsterdam; Tinbergen Institute; Tilburg University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2011.05.014
• 发表日期: 2012
• 页码: 434-441
• 关键词: Evolutionary games; Logit dynamics; Hopf bifurcation; Fold bifurcation

摘要

This note shows, by means of two simple, three-strategy games, the existence of stable periodic orbits and of multiple, interior steady states in a smooth version of the Best-Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cycles, occur under the Logit Dynamics, even for three-strategy games. We also show that the Logit Dynamics displays another bifurcation which cannot occur under the Replicator Dynamics: the fold bifurcation, with non-monotonic creation and disappearance of steady states. (C) 2011 Elsevier Inc. All rights reserved.