Large games and the law of large numbers
成果类型：
Article
署名作者：
Al-Najjar, Nabil I.
署名单位：
Northwestern University
刊物名称：
GAMES AND ECONOMIC BEHAVIOR
ISSN/ISSBN：
0899-8256
DOI：
10.1016/j.geb.2007.11.002
发表日期：
2008
页码：
1-34
关键词：
摘要：
This paper introduces discrete large games where the set of players is a countable dense 'grid' with a finitely additive distribution. In these games an), function from player names to mixed actions is a legitimate strategy profile. No extraneous continuity or measurability conditions are assumed. Randomness can be modeled explicitly and ail exact law of large numbers holds. Equilibria enjoy a strong purification property: every realization of every mixed strategy equilibrium is a pure strategy equilibrium almost surely. Every continuum-player game has a discrete large game representation that preserves the original payoffs, strategy profiles and equilibria. It is argued that strategy profiles in continuum-player games have an ambiguous meaning because measurability requirements force the smoothing out of individual variations. These variations have clear strategic meaning in finite-player games and can be expressed in discrete large games, but not when the set of players is the continuum. (c) 2008 Elsevier Inc. All rights reserved.