Long time behaviour of Mean Field Games with fractional diffusion

2025/05/09 by Olav Ersland, Espen R. Jakobsen, Ersland, Olav +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2505.06183

Abstract

In this paper we study the long time behaviour of mean field games systems with fractional diffusion, modeling the case that the individual dynamics of the players is driven by independent jump processes and controlled through the drift term, while being confined by an external field in order to guarantee ergodicity. In the case of globally Lipschitz, locally uniformly convex Hamiltonian, and weakly coupled costs satisfying the Lasry-Lions monotonicity condition, we prove that there is a unique solution (u_T,m_T) to the mean field game problem in (0,T) and we show that, if T is sufficiently large, (u_T,m_T) satisfies the so-called turnpike property, namely it is exponentially close to the (unique) stationary ergodic state for any proportionally long intermediate time.

Cited by

• System-Theoretic Analysis of Dynamic Generalized Nash Equilibrium Problems -- Turnpikes and Dissipativity
• Mean Field Games of Controls with Fractional Laplacian

Related

• Long time behaviour and turnpike solutions in mildly non-monotone mean field games
• The exponential turnpike phenomenon for mean field game systems: weakly monotone drifts and small interactions
• Long-time behaviour of deterministic Mean Field Games with non-monotone interactions
• Long Time Behavior and Stabilization for Displacement Monotone Mean Field Games
• A time-fractional mean field game