Functional Analytic Insights into Mean Field Game Theory

Giovedì 23 maggio alle 16, nell’aula G del Dipartimento di Matematica e Informatica si tiene il seminario "Functional Analytic Insights into Mean Field Game Theory" di Diogo Gomes, docente della King Abdullah University of Science and Technology 

Abstract

Monotonicity conditions are crucial in Mean Field Game (MFG) theory, highlighted by Larry and Lions' uniqueness results. 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. Finally, we also address the question of uniqueness of solutions for weak solutions.

(23 maggio 2024)