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 (regular enough) solution provides an (Formula presented.) -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 McKean-Vlasov SPDEs and the (Formula presented.) -convergence rate for the propagation of chaos property of interacting diffusions.

Original languageEnglish
Pages (from-to)522-549
Number of pages28
JournalStochastic Analysis and Applications
Issue number4
Publication statusPublished - 4 Jul 2019

Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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