LONG TIME AVERAGE OF MEAN FIELD GAMES WITH A NONLOCAL COUPLING?

摘要

We study the long time average, as the time horizon tends to infinity, of the solution of a mean field game system with a nonlocal coupling. We show an exponential convergence to the solution of the associated stationary ergodic mean field game. Proofs rely on semiconcavity estimates and smoothing properties of the linearized system.