ON FIRST ORDER MEAN FIELD GAME SYSTEMS WITH A COMMON NOISE

• 成果类型: Article
• 署名作者: Cardaliaguet, Pierre; Souganidis, Panagiotis E.
• 署名单位: Universite PSL; Universite Paris-Dauphine; University of Chicago
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1734
• 发表日期: 2022
• 页码: 2289-2326
• 关键词: differential-equations; VISCOSITY SOLUTIONS; cauchy-problem; uniqueness; PRINCIPLE

摘要

We consider mean field games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution exists and is unique for monotone coupling functions. We also use the solution to find approximate optimal strategies (Nash equilibria) for N-player differential games with common but no idiosyncratic noise. An important step in the analysis is the study of the well-posedness of a stochastic backward Hamilton-Jacobi equation.