Stable games and their dynamics

• 成果类型: Article
• 署名作者: Hofbauer, Josef; Sandholm, William H.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of Vienna
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2009.01.007
• 发表日期: 2009
• 页码: 1665-1693
• 关键词: Population games; Evolutionarily stable strategies; evolutionary dynamics; Global stability; Lyapunov functions

摘要

We study a class of population games called stable games. These games are characterized by self-defeating externalities: when agents revise their strategies, the improvements in the payoffs of strategies to which revising agents are switching are always exceeded by the improvements in the payoffs of strategies which revising agents are abandoning. We prove that the set of Nash equilibria of a stable game is globally asymptotically stable under a wide range of evolutionary dynamics. Convergence results for stable games are not as general as those for potential games: in addition to monotonicity of the dynamics, integrability of the agents' revision protocols plays a key role. (C) 2009 Elsevier Inc. All rights reserved.