Universality of Nash components

• 成果类型: Article
• 署名作者: Balkenborg, Dieter; Vermeulen, Dries
• 署名单位: University of Exeter; Maastricht University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2014.03.010
• 发表日期: 2014
• 页码: 67-76
• 关键词: Strategic form games; Nash equilibrium; Nash component; TOPOLOGY

摘要

We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game-a game where all players have two pure strategies and a common utility function with values either zero or one-whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets. We discuss implications of our results for the strategic stability of success sets, and use the results to construct a Nash component with index k for any fixed integer k. (C) 2014 Elsevier Inc. All rights reserved.