| Abstract: |
| In this talk, we address the question of uniqueness of weak solutions for 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. |
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