Cours FSMP - Chaire Finance & Développement Durable sur la théorie des jeux à champs moyens
Alessio Porretta (Università di Roma Tor Vergata) a donné un cours dans le cadre d'une collaboration entre la Chaire Finance et Développement Durable et le LabEx SMP. Ce cours a porté sur la théorie des jeux à champs moyens.
Il s'est tenu à l'Institut Henri Poincaré (11 rue Pierre et Marie Curie - Paris 5ème) en mars et avril 2015.
Résumé du cours :
Mean field games theory was initiated by J.-M. Lasry and P.-L. Lions since 2006 in order to describe control processes with large number of agents (say, a population of identical individuals) whose strategy is influenced by the overall distribution of the agents. The macroscopic description, suggested as an asymptotic regime of Nash equilibria of N-players games when N goes to infinity, is given in terms of a new system of PDEs, where a backward Hamilton-Jacobi-Bellman equation (describing the individual strategy) is coupled with a forward Kolmogorov-Fokker-Planck equation (describing the evolution of the distribution law). The goal of this course is to present several problems and methods recently developed in the study of those systems, addressing questions such as the long time behavior and its connection with the turnpike property of controlled systems, the optimal transport of the distribution law, the well-posedness of weak theories and other possible related directions of research.