Analysis of mean field games via Fokker-Planck-Kolmogorov equations: existence of equilibria

TL;DR

This paper investigates mean field games with unbounded coefficients, establishing the existence of solutions using a novel approach involving Fokker-Planck-Kolmogorov equations and advanced mathematical techniques.

Contribution

It introduces a new method for proving the existence of equilibria in mean field games with unbounded coefficients, expanding the theoretical framework.

Findings

Existence of solutions for mean field games with unbounded coefficients

Development of a new analytical approach using Fokker-Planck-Kolmogorov equations

Application of superposition principle and Lyapunov functions for estimates

Abstract

We study mean field games with unbounded coefficients. The existence of a solution is proved. We propose a new approach based on Fokker-Planck-Kolmogorov equations, the Ambrosio-Figalli-Trevisan superposition principle, the method of doubling variables and a~priory estimates with Lyapunov functions.