On the closed-graph property of the Nash equilibrium correspondence in a large game: A complete characterization

• 成果类型: Article
• 署名作者: Qiao, Lei; Yu, Haomiao; Zhang, Zhixiang
• 署名单位: Shanghai University of Finance & Economics; Toronto Metropolitan University; Central University of Finance & Economics
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2016.07.007
• 发表日期: 2016
• 页码: 89-98
• 关键词: Closed-graph property; Large game with traits (LGT); Lebesgue unit interval; Nash equilibrium; Nash equilibrium distribution; saturated probability space

摘要

We show that if every large game with a given player space and any given uncountable trait space (or action set) is a proper idealized limit, then the player space must be saturated. When the player space is allowed to be an arbitrary atomless probability space, even a non-saturated one such as the classical Lebesgue unit interval, we establish the following: (i) If a large game has a countable action set and a countable trait space, then the game has a closed Nash equilibrium correspondence, and is thus proper as an idealized limit; (ii) If every large game having a given action set and a given trait space is proper as an idealized limit, then both the action set and the trait space must be countable. (C) 2016 Elsevier Inc. All rights reserved.