Nash equilibrium and generalized integration for infinite normal form games

• 成果类型: Article
• 署名作者: Stinchcombe, MB
• 署名单位: University of Texas System; University of Texas Austin
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2004.09.007
• 发表日期: 2005
• 页码: 332-365
• 关键词: Infinite games; equilibrium; nonmeasurable integration; compactification; selection equilibria

摘要

Infinite normal form games that are mathematically simple have been treated [ Harris, C.J., Stinch-combe, M.B., Zame, W.R., in press. Nearly compact and continuous normal form games: characterizations and equilibrium existence. Games Econ. Behav.]. Under study in this paper are the other infinite normal form games, a class that includes the normal forms of most extensive form games with infinite choice sets. Finitistic equilibria are the limits of approximate equilibria taken along generalized sequences of finite subsets of the strategy spaces. Points must be added to the strategy spaces to represent these limits. There are direct, nonstandard analysis, and indirect, compactification and selection, representations of these points. The compactification and selection approach was introduced [Simon, L.K., Zame, W.R., 1990. Discontinuous games and endogenous sharing rules. Econometrica 58, 861-872]. It allows for profitable deviations and introduces spurious correlation between players' choices. Finitistic equilibria are selection equilibria without these drawbacks. Selection equilibria have drawbacks, but contain a set-valued theory of integration for non-measurable functions tightly linked to, and illuminated by, the integration of correspondences. (C) 2004 Elsevier Inc. All rights reserved.