Large games with a bio-social typology

• 成果类型: Article
• 署名作者: Khan, M. All; Rath, Kali P.; Sun, Yeneng; Yu, Haomiao
• 署名单位: Johns Hopkins University; University of Notre Dame; National University of Singapore; Toronto Metropolitan University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2012.11.002
• 发表日期: 2013
• 页码: 1122-1149
• 关键词: Large games; Social-type; traits; Idealized limit game; saturated probability space; Pure-strategy Nash equilibrium; Closed-graph property; Upper hemi-continuity; asymptotic implementation

摘要

We present a comprehensive theory of large games in which players have names and determinate social-types and/or biological traits, and identify through four decisive examples, essentially based on a matching-pennies type game, pathologies arising from the use of a Lebesgue interval for player's names. In a sufficiently general context of traits and actions, we address this dissonance by showing a saturated probability space as being a necessary and sufficient name-space for the existence and upper hemi-continuity of pure-strategy Nash equilibria in large games with traits. We illustrate the idealized results by corresponding asymptotic results for an increasing sequence of finite games. (C) 2013 Elsevier Inc. All rights reserved.