Better-reply dynamics and global convergence to Nash equilibrium in aggregative games

• 成果类型: Article
• 署名作者: Dindos, M; Mezzetti, C
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Brown University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2004.12.001
• 发表日期: 2006
• 页码: 261-292
• 关键词: Aggregative games; better-reply dynamics; Strategic complements; Strategic substitutes; weak finite improvement property

摘要

We consider n-person games with quasi-concave payoffs that depend on a player's own action and the sum of all players' actions. We show that a discrete-time, stochastic process in which players move towards better replies-the better-reply dynamics-converges globally to a Nash equilibrium if actions are either strategic substitutes or strategic complements for all players around each Nash equilibrium that is asymptotically stable under a deterministic, adjusted best-reply dynamics. We present an example of a 2-person game with a unique equilibrium where the derivatives of the best-reply functions have different signs and the better-reply dynamics does not converge. (c) 2005 Elsevier Inc. All rights reserved.