On first order mean field game systems with a common noise
Cardaliaguet, Pierre; Souganidis, Panagiotis E. (2022), On first order mean field game systems with a common noise, Annals of Applied Probability, 32, 3, p. 2289-2326. 10.1214/21-AAP1734
TypeArticle accepté pour publication ou publié
Journal nameAnnals of Applied Probability
Institute of Mathematical Statistics
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Souganidis, Panagiotis E.
Department of Mathematics [Chicago]
Abstract (EN)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. This the first general result for solutions of the Mean Field Games system with common and no idiosynctratic noise. 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.
Subjects / KeywordsMean Field Games; Hamilton-Jacobi equation; Backward stochastic partial differential equations; common noise; maximum principle
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