@article{4520d5e945f64f1da4c895bdfa97d650,
title = "CONTROLLED DIFFUSION MEAN FIELD GAMES WITH COMMON NOISE AND MCKEAN–VLASOV SECOND ORDER BACKWARD SDEs",
abstract = "We consider a mean field game with common noise in which the diffusion coefficients may be controlled. We prove existence of a weak relaxed solution under some continuity conditions on the coefficients. We then show that, when there is no common noise, the solution of this mean field game is characterized by a McKean–Vlasov type second order backward SDE.",
keywords = "exterior noise, mean field game, Nash equilibrium, stochastic control",
author = "A. Barrasso and N. Touzi",
note = "Funding Information: ∗Received by the editors June 30, 2021. This work was supported by ANR project PACMAN, the joint lab FiME, the Chaires FiME-FDD, and Financial Risks of the Louis Bachelier Institute. Originally published in the Russian journal Teoriya Veroyatnostei i ee Primeneniya, 66 (2021), pp. 774–805. https://doi.org/10.1137/S0040585X97T990654 †Universit{\'e}d{\textquoteright}{\'E}vry Val d{\textquoteright}Essonne, {\'E}vry, France (adrien.barrasso@univ-evry.fr). ‡Ecole Polytechnique, France (nizar.touzi@polytechnique.edu). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",
year = "2022",
doi = "10.1137/S0040585X97T990654",
language = "English (US)",
volume = "66",
pages = "613--639",
journal = "Theory of Probability and its Applications",
issn = "0040-585X",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}