THE EMERGENCE OF RATIONAL BEHAVIOR IN THE PRESENCE OF STOCHASTIC PERTURBATIONS

• 成果类型: Article
• 署名作者: Mertikopoulos, Panayotis; Moustakas, Aris L.
• 署名单位: National & Kapodistrian University of Athens
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP651
• 发表日期: 2010
• 页码: 1359-1388
• 关键词: replicator dynamics; games

摘要

We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the replicator dynamics that is quite different from the aggregate shocks approach of evolutionary game theory. Irrespective of the perturbations' magnitude, we find that strategies which are dominated (even iteratively) eventually become extinct and that the game's strict Nash equilibria are stochastically asymptotically stable. We complement our analysis by illustrating these results in the case of congestion games.