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On the mean field games with common noise and the McKean-Vlasov SPDEs
Vassili Kolokoltsov, Marianna Troeva · 2015-06-15 · via math.PR updates on arXiv.org

We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution provides an $1/N$-Nash-equilibrium profile for the initial $N$-player game. We use the method of stochastic characteristics to provide the link with the basic models of MFG with a major player. We develop two auxiliary theories of independent interest: sensitivity and regularity analysis for the McKean-Vlasov SPDEs and the $1/N$-convergence rate for the propagation of chaos property of interacting diffusions.

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