CONVERGENCE TO THE MEAN FIELD GAME LIMIT: A CASE STUDY

• 成果类型: Article
• 署名作者: Nutz, Marcel; San Martin, Jaime; Tan, Xiaowei
• 署名单位: Columbia University; Columbia University; Universidad de Chile; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1501
• 发表日期: 2020
• 页码: 259-286
• 关键词: n-player games

摘要

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of n-player equilibria converges to it as n -> infinity. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of n-player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not limits, thus questioning their interpretation as large n equilibria.