Existence of Nash equilibrium in games with a measure space of players and discontinuous payoff functions

• 成果类型: Article
• 署名作者: Carmona, Guilherme; Podezeck, Konrad
• 署名单位: University of Surrey; University of Vienna
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2014.04.002
• 发表日期: 2014
• 页码: 130-178
• 关键词: Nash equilibrium; discontinuous games; Large games

摘要

Balder's [6] model of games with a measure space of players is integrated with the line of research on finite-player games with discontinuous payoff functions which follows Reny [47]. Specifically, we extend the notion of continuous security, introduced by McLennan, Monteiro & Tourky [38] and Barelli & Meneghel [9] for finite-players games, to games with a measure space of players and establish the existence of pure strategy Nash equilibrium for such games. A specification of our main existence result is provided which is ready to fit the needs of applications. As an illustration, we consider several optimal income tax problems in the spirit of Minlees [40] and use our game-theoretic result to show the existence of an optimal income tax in each of these problems. (C) 2014 Elsevier Inc. All rights reserved.