TY - JOUR

T1 - On mean field games with common noise and McKean-Vlasov SPDEs

AU - Kolokoltsov, Vassili N.

AU - Troeva, Marianna

PY - 2019/7/4

Y1 - 2019/7/4

N2 - 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.

AB - 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.

KW - common noise

KW - interacting particles

KW - McKean-Vlasov SPDE

KW - Mean-field games

KW - sensitivity

UR - http://www.scopus.com/inward/record.url?scp=85064640958&partnerID=8YFLogxK

U2 - 10.1080/07362994.2019.1592690

DO - 10.1080/07362994.2019.1592690

M3 - Article

AN - SCOPUS:85064640958

VL - 37

SP - 522

EP - 549

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

SN - 0736-2994

IS - 4

ER -