On the evolutionary selection of sets of Nash equilibria

• 成果类型: Article
• 署名作者: Balkenborg, Dieter; Schlag, Karl H.
• 署名单位: University of Exeter; European University Institute
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2005.08.008
• 发表日期: 2007
• 页码: 295-315
• 关键词: evolutionary dynamics; Replicator dynamic; regular selection dynamics; strict equilibrium set; Nash equilibrium component

摘要

It is well established for evolutionary dynamics in asymmetric games that a pure strategy combination is asymptotically stable if and only if it is a strict Nash equilibrium. We use an extension of the notion of a strict Nash equilibrium to sets of strategy combinations called 'strict equilibrium set' and show the following. For a large class of evolutionary dynamics, including all monotone regular selection dynamics, every asymptotically stable set of rest points that contains a pure strategy combination in each of its connected components is a strict equilibrium set. A converse statement holds for two-person games, for convex sets and for the standard replicator dynamic. (c) 2005 Elsevier Inc. All rights reserved.