Individually rational pure strategies in large games

• 成果类型: Article
• 署名作者: Stanford, W
• 署名单位: University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/S0899-8256(03)00142-8
• 发表日期: 2004
• 页码: 221-233
• 关键词: Individual rationality; bounded rationality; folk theorem; repeated games; minimax payoffs; pure strategy; approximate equilibrium

摘要

In randomly selected large finite normal form games, pure strategy strongly individually rational outcomes (all payoffs exceeding pure strategy minimax payoffs) exist with high probability. As a corollary, pure strategy Nash equilibria also exist with high probability in certain infinitely repeated games. Specifically, the pure strategy Folk Theorem, which can be true in a vacuous sense, has nontrivial substance with probability approaching one as pure strategy sets increase in cardinality, provided strategy set growth rates are not too different. To prove this, and noting a possible bounded rationality interpretation, we begin with a study of approximate equilibria in finite normal form games. Given a positive integer 1, these are pure strategy outcomes where each player's payoff is among the I largest available given strategy choices of opponents. When pure strategy sets are large, such outcomes are highly probable and usually have payoffs dominating pure minimax payoffs. (C) 2003 Elsevier Inc. All rights reserved.