Mean field game PDE systems were introduced by J-M. Lasry and P.-L. Lions to describe Nash equilibria in multi-agents dynamic optimization. In the simplest model, those are forward-backward systems coupling Hamilton-Jacobi with Fokker-Planck equations. In this talk I will discuss the long time behavior of second order systems in the periodic case under suitable stability conditions. I will go through the main features that appear in the study of the long time limit: the ergodic behavior, the effects of the forward-backward structure, the exponential turnpike property of the underlying control problem and the link with the vanishing discount limit in infinite horizon problems.

Zoom meeting: Link – pass: 1234