Imitative dynamics for games with continuous strategy space

• 成果类型: Article
• 署名作者: Cheung, Man-Wah
• 署名单位: Shanghai University of Finance & Economics
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2016.08.003
• 发表日期: 2016
• 页码: 206-223
• 关键词: Imitative dynamics; Replicator dynamic; Payoff monotonicity; Continuous strategy space

摘要

This paper studies imitative dynamics for games with continuous strategy space. We define imitative dynamics which include the replicator dynamic as a special case as evolutionary dynamics that satisfy the imitative property and payoff monotonicity. Our definition of payoff monotonicity, which we use Radon-Nikodym derivatives to define, is weaker than the one proposed in Oechssler and Riedel (2002). We find that Oechssler and Riedel (2002)'s definition is too strong, and our definition is more adequate than theirs. We show that for a broad class of payoff functional dynamics, payoff monotonicity a la Oechssler and Riedel (2002) is equivalent to aggregate monotonicity in the sense of Samuelson and Zhang (1992). We then provide sufficient conditions for imitative dynamics and general evolutionary dynamics to be well-defined. Finally, with our definition of payoff monotonicity, a number of results that are standard for finite games extend to the case of games with continuous strategy space. (C) 2016 Elsevier Inc. All rights reserved.