Oddness of the number of Nash equilibria: The case of polynomial payoff functions

• 成果类型: Article
• 署名作者: Bich, Philippe; Fixary, Julien
• 署名单位: Paris School of Economics
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2024.04.005
• 发表日期: 2024
• 页码: 510-525
• 关键词: Nash equilibrium; Polynomial payoff functions; Generic oddness; Network games

摘要

In 1971, Wilson (1971) proved that almost all finite games have an odd number of mixed Nash equilibria. Since then, several other proofs have been given, but always for mixed extensions of finite games. In this paper, we present a new oddness theorem for large classes of polynomial payoff functions and semi -algebraic sets of strategies. Additionally, we provide some applications to recent models of games on networks such that Patacchini-Zenou's model about juvenile delinquency and conformism (Patacchini and Zenou, 2012), Calv & oacute;-Armengol-Patacchini-Zenou's model about social networks in education (Calv & oacute;-Armengol et al., 2009), Konig-Liu-Zenou's model about R&D networks (K & ouml;nig et al., 2019), Helsley-Zenou's model about social networks and interactions in cities (Helsley and Zenou, 2014).