MEAN FIELD GAMES WITH COMMON NOISE AND DEGENERATE IDIOSYNCRATIC NOISE

• 成果类型: Article
• 署名作者: Cardaliaguet, Pierre; Seeger, Benjamin; Souganidis, Panagiotis
• 署名单位: Universite PSL; Universite Paris-Dauphine; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of Chicago
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/25-AAP2148
• 发表日期: 2025
• 关键词: viscosity solutions; EQUATIONS

摘要

We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that the idiosyncratic noise coefficient may be degenerate, so that the system does not admit smooth solutions in general. We develop a new notion of weak solutions for backward stochastic Hamilton-Jacobi-Bellman equations, and use this to build probabilistically weak solutions of the mean field game system. Under an additional monotonicity assumption, we prove the uniqueness of a strong solution.