Abstract: 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. In particular, we give explicit conditions under which this uniqueness holds.

About the Speaker: Diogo Gomes is Professor of Applied Mathematics and Computational Science (AMCS) in KAUST, and from 2018 also Chair of the AMCS Program. Gomes' research interests are in partial differential equations (PDE), namely on viscosity solutions of elliptic, parabolic and Hamilton-Jacobi equations as well as in related mean-field models. Applications of his work include from computer vision to population dynamics and numerical methods.