Diogo Gomez, "Functional Analytic Insights into Mean Field Game Theory", Dip. Matematica
Seminario di Modellistica Differenziale Numerica
Sala di Consiglio, Dipartimento di Matematica "G. Castelnuovo"
Oratore: Diogo Gomez (KAUST)
Titolo: Functional Analytic Insights into Mean Field Game Theory
Abstract: Monotonicity conditions are crucial in Mean Field Game (MFG) theory, highlighted by the uniqueness results of Larry and Lions. This talk introduces a functional analytic framework to understand MFGs that satisfy monotonicity conditions. By leveraging ideas introduced in Hessian-Riemannian flows from optimization, we propose regularized versions of MFGs and construct contracting flows that can be used for numerical approximation. Our findings present a consolidated view of our prior works and give a different perspective on this class of problems.