ON THE CONNECTION BETWEEN SYMMETRIC N-PLAYER GAMES AND MEAN FIELD GAMES

• 成果类型: Article
• 署名作者: Fischer, Markus
• 署名单位: University of Padua
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1215
• 发表日期: 2017
• 页码: 757-810
• 关键词: nonlinear parabolic equations

摘要

Mean field games are limit models for symmetric N-player games with interaction of mean field type as N -> infinity. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate Nash equilibria for the corresponding N-player games. The opposite direction is of interest, too: When do sequences of Nash equilibria converge to solutions of an associated mean field game? In this direction, rigorous results are mostly available for stationary problems with ergodic costs. Here, we identify limit points of sequences of certain approximate Nash equilibria as solutions to mean field games for problems with Ito-type dynamics and costs over a finite time horizon. Limits are studied through weak convergence of associated normalized occupation measures and identified using a probabilistic notion of solution for mean field games.