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

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• 作者：Martin Dindoš ; and Claudio Mezzetti
• 关键词：Aggregative games ; Better-reply dynamics ; Strategic complements ; Strategic substitutes ; Weak finite improvement property
• 刊名：Games and Economic Behavior
• 出版年：2006
• 出版时间：February 2006
• 年：2006
• 卷：54
• 期：2
• 页码：261-292
• 全文大小：284 K

文摘

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.