Uniform payoff security and Nash equilibrium in compact games

• 成果类型: Article
• 署名作者: Monteiro, Paulo Klinger; Page, Frank H., Jr.
• 署名单位: University of Alabama System; University of Alabama Tuscaloosa
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2006.01.007
• 发表日期: 2007
• 页码: 566-575
• 关键词: uniform payoff security; Nash equilibrium; discontinuous games; mixed extension

摘要

We introduce a condition, uniform payoff security, for games with compact Hausdorff strategy spaces and payoffs bounded and measurable in players' strategies. We show that if any such compact game G is uniformly payoff secure, then its mixed extension (G) over bar is payoff secure. We also establish that if a uniformly payoff secure compact game G has a mixed extension (G) over bar with reciprocally upper semicontinuous payoffs, then G has a Nash equilibrium in mixed strategies. We provide several economic examples of compact games satisfying uniform payoff security. (c) 2006 Elsevier Inc. All rights reserved.