TY - JOUR

T1 - On mean field games with common noise based on stable-like processes

AU - Kolokoltsov, Vassili N.

AU - Troeva, Marianna

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper, we study Mean Field Games with common noise based on nonlinear stable-like processes. The MFG limit is specified by a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. The main result is that any its solution provides an 1/N-Nash equilibrium for the initial game of N agents. Our approach is based on interpreting the common noise as a kind of binary interaction of agents and our previous results on regularity and sensitivity with respect to the initial conditions of the solution to the nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes.

AB - In this paper, we study Mean Field Games with common noise based on nonlinear stable-like processes. The MFG limit is specified by a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. The main result is that any its solution provides an 1/N-Nash equilibrium for the initial game of N agents. Our approach is based on interpreting the common noise as a kind of binary interaction of agents and our previous results on regularity and sensitivity with respect to the initial conditions of the solution to the nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes.

KW - McKean-Vlasov SPDE

KW - Mean-field games with common noise

KW - Nash equilibrium

KW - Regularity

KW - Sensitivity

KW - Stable-like processes

UR - http://www.scopus.com/inward/record.url?scp=85065970949&partnerID=8YFLogxK

U2 - 10.19139/soic.v7i2.637

DO - 10.19139/soic.v7i2.637

M3 - Article

AN - SCOPUS:85065970949

VL - 7

SP - 264

EP - 276

JO - Statistics, Optimization and Information Computing

JF - Statistics, Optimization and Information Computing

SN - 2311-004X

IS - 2

ER -