TIME AVERAGES, RECURRENCE AND TRANSIENCE IN THE STOCHASTIC REPLICATOR DYNAMICS

• 成果类型: Article
• 署名作者: Hofbauer, Josef; Imhof, Lorens A.
• 署名单位: University of Vienna; University of Bonn; University of Bonn
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP577
• 发表日期: 2009
• 页码: 1347-1368
• 关键词: Evolutionary game dynamics; urn models; BEHAVIOR

摘要

We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and Nash equilibria of a suitably modified game. Furthermore, a sufficient condition for transience is given in terms of mixed equilibria and definiteness of the payoff matrix. We also present necessary and sufficient conditions for stochastic stability of pure equilibria.