Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics

• 成果类型: Article
• 署名作者: Sandholm, William H.; Staudigl, Mathias
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; Maastricht University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2017.0908
• 发表日期: 2018
• 页码: 1348-1377
• 关键词: stationary distributions; differential-equations; recursive algorithms; long-run; STABILITY; equilibria; LIMITS

摘要

We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of decay of the probability that the sample path of the evolutionary process lies in a prespecified set as the population size approaches infinity. We use these results to describe excursion rates and stationary distribution asymptotics in settings where the mean dynamic admits a globally attracting state, and we compute these rates explicitly for the case of logit choice in potential games.