On the equivalence of large individualized and distributionalized games

• 成果类型: Article
• 署名作者: Khan, Mohammed Ali; Rath, Kali P.; Yu, Haomiao; Zhang, Yongchao
• 署名单位: Johns Hopkins University; University of Notre Dame; Toronto Metropolitan University; Shanghai University of Finance & Economics
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE1806
• 发表日期: 2017-05-01
• 页码: 533-554
• 关键词: Distributionalized games; individualized games; Nash equilibrium distribution; Nash equilibrium; REPRESENTATION; EQUIVALENCE; weak equivalence; quasi-equivalence; realization; Similarity; symmetry; countability; saturation

摘要

The theory of large one-shot simultaneous-play games with a biosocial typology has been presented in both the individualized and distributionalized forms-large individualized games (LIG) and large distributionalized games (LDG), respectively. Using an example of an LDG with two actions and a single trait in which some Nash equilibrium distributions cannot be induced by the Nash equilibria of the representing LIG, this paper offers three equivalence results that delineate a relationship between the two game forms. Our analysis also reveals the different roles that the Lebesgue unit interval and a saturated space play in the theory.