Abstract
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.
Funding Statement
P.Cardaliaguet was partially supported by AFOSR Grant FA9550-18-1-0494. P. E. Souganidis was partially supported by NSF Grants DMS-1600129 and DMS-1900599, ONR Grant N000141712095 and AFOSR Grant FA9550-18-1-0494.
Citation
Pierre Cardaliaguet. Panagiotis E. Souganidis. "On first order mean field game systems with a common noise." Ann. Appl. Probab. 32 (3) 2289 - 2326, June 2022. https://doi.org/10.1214/21-AAP1734
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