A PROBABILISTIC WEAK FORMULATION OF MEAN FIELD GAMES AND APPLICATIONS

• 成果类型: Article
• 署名作者: Carmona, Rene; Lacker, Daniel
• 署名单位: Princeton University; Princeton University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1020
• 发表日期: 2015
• 页码: 1189-1231
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; BEHAVIOR; limit

摘要

Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to include rank and nearest-neighbor effects. Moreover, the data may depend discontinuously on the state variable, and more generally its entire history. Existence and uniqueness results are proven, along with a procedure for identifying and constructing distributed strategies which provide approximate Nash equlibria for finite-player games. Our results are applied to a new class of multi-agent price impact models and a class of flocking models for which we prove existence of equilibria.