{"ID":2880393,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.15029","arxiv_id":"2508.15029","title":"Analysis of mean field games via Fokker-Planck-Kolmogorov equations: existence of equilibria","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.","short_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.","url_abs":"https://arxiv.org/abs/2508.15029","url_pdf":"https://arxiv.org/pdf/2508.15029v2","authors":"[\"Stanislav V. Shaposhnikov\",\"Dmitry V. Shatilovich\"]","published":"2025-08-20T19:46:44Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OC\",\"math.PR\"]","methods":"[]","has_code":false}