Quadratic Mean Field Games with Negative Coordination
par
Thibault Bonnemain
Jury:
Cécile APPERT-ROLLAND, Univeristé Paris-Saclay, examinatrice
Thierry GOBRON, Université Cergy-Pontoise, directeur de thèse
Olivier GUEANT, Université Paris 1 Panthéon-Sorbonne, examinateur
Max-Olivier HONGLER, EPFL, rapporteur
Jean-Pierre NADAL, École Normale Supérieure, examinateur
Filippo SANTAMBROGIO, Université Claude Bernard – Lyon 1, rapporteur
Denis ULLMO, Univeristé Paris-Saclay, co-directeur de thèse
Resumé:
Mean Field Games provide a powerful theoretical framework to deal with stochastic optimization problems involving a large number of coupled subsystems. They can find application in several fields, be it finance, economy, sociology, engineering … However, this theory is rather recent and still poses many challenges. Its constitutive equations, for example, are difficult to analyse and the set of behaviours they highlight are ill-understood. While the large majority of contributions to this discipline come from mathematicians, economists or engineering scientists, physicist have only marginally be involved in it. In this thesis I try and start bridging the gap between Physics and Mean Field Games through the study of a specific class of models dubbed « quadratic ».