MEAN FIELD GAMES WITH COMMON NOISE

• 成果类型: Article
• 署名作者: Carmona, Rene; Delarue, Francois; Lacker, Daniel
• 署名单位: Princeton University; Princeton University; Universite Cote d'Azur; Universite Cote d'Azur
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1060
• 发表日期: 2016
• 页码: 3740-3803
• 关键词: Existence; systems

摘要

A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential equations, and existence of weak solutions for mean field games is shown to hold under very general assumptions. Examples and counter-examples are provided to enlighten the underpinnings of the existence theory. Finally, an analog of the famous result of Yamada and Watanabe is derived, and it is used to prove existence and uniqueness of a strong solution under additional assumptions.