On the long time convergence of potential MFG

Marco Masoero (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales

We look at the long time behavior of potential Mean Field Games (briefly MFG) using some standard tools from weak KAM theory. We first show that the time-dependent minimization problem converges to an ergodic constant −λ, then we provide a class of examples where the value of the stationary MFG minimization problem is strictly greater than −λ. This will imply that the trajectories of the time-dependent MFG system do not converge to static equilibria.

Domaines: Optimisation et contrôle [math.OC]

Marco Masoero. On the long time convergence of potential MFG. 2018. ⟨hal-01850874⟩