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

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.