Weak-strong uniqueness for mean-field games

par D. Gomes

mercredi 5 juin 2024, 10:20 → 11:00 Europe/Paris

XR 203 (XLIM)

We address the uniqueness of stationary first-order Mean-Field Games
(MFGs). Despite well-established existence results, establishing uniqueness, particularly for weaker solutions in the sense of monotone operators, remains an open challenge. Building upon the framework of monotonicity methods, we introduce a linearization method that enables us to prove a weak-strong  uniqueness result for stationary MFG systems on the d-dimensional torus. In particular, we give explicit conditions under which this uniqueness holds.