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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.
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[author] Bayraktar, ErhanE., Cecchin, AlekosA., Cohen, AsafA. and Delarue, FrançoisF. (2021). Finite state mean field games with Wright-Fisher common noise. J. Math. Pures Appl. (9) 147 98–162. 10.1016/j.matpur.2021.01.003 4213680
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[author] Bertucci, CharlesC. (2021). Monotone solutions for mean field games master equations: finite state space and optimal stopping. J. Éc. polytech. Math. 8 1099–1132. 10.5802/jep.167 4275225
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[author] Flandoli, F.F., Gubinelli, M.M. and Priola, E.E. (2010). Well-posedness of the transport equation by stochastic perturbation. Invent. Math. 180 1–53. 10.1007/s00222-009-0224-4 2593276
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[author] Qiu, JinniaoJ. (2018). Viscosity solutions of stochastic Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 56 3708–3730. 10.1137/17M1148232 3864678
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[author] Bertucci, CharlesC., Lasry, Jean-MichelJ.-M. and Lions, Pierre-LouisP.-L. (2021). Master equation for the finite state space planning problem. Arch. Ration. Mech. Anal. 242 327–342. 10.1007/s00205-021-01687-8 4302761
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[author] Cardaliaguet, PierreP. and Souganidis, PanagiotisP. (2022). Monotone solutions of the master equation for mean field games with idiosyncratic noise. SIAM J. Math. Anal. 54 4198–4237. 10.1137/21M1450008 4451309
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[author] Cardaliaguet, PierreP. and Souganidis, Panagiotis E.P. E. (2022). On first order mean field game systems with a common noise. Ann. Appl. Probab. 32 2289–2326. 10.1214/21-aap1734 4430014
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[author] Bertucci, CharlesC. (2023). Monotone solutions for mean field games master equations: continuous state space and common noise. Comm. Partial Differential Equations 48 1245–1285. 10.1080/03605302.2023.2276564 4687277
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[author] Djete, Mao FabriceM. F. (2023). Large population games with interactions through controls and common noise: convergence results and equivalence between open-loop and closed-loop controls. ESAIM Control Optim. Calc. Var. 29 Paper No. 39, 42. 10.1051/cocv/2023005 4598796
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[author] Mou, ChenchenC. and Zhang, JianfengJ. (2024). Wellposedness of second order master equations for mean field games with nonsmooth data. Mem. Amer. Math. Soc. 302 v+86. 10.1090/memo/1515 4813035
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