Il professor
Luciano Campi
della London School of Economics and Political Science (LSE)
terrà un seminario dal titolo
Mean-field games with absorption
il giorno
lunedì 11 febbraio 2019 alle ore 14:00
in sala rappresentanza del Dipartimento di Matematica dell'Università di Milano (via Saldini 50, 20133 Milano).
Tutti gli interessati sono cordialmente invitati.
Cordiali saluti, Marco Fuhrman
Abstract. We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding N-player games, the dynamics of players' states follows a system of weakly interacting Ito equations with absorption on first exit from a given set. Once a player leaves the game, her/his contribution is removed from the empirical measure of the system. Players thus interact through a renormalized empirical measure. In the definition of solution to the mean field game, the renormalization appears in form of a conditional law. We also consider the case of a system whose drift can be affected by the fraction of past absorbed players. Under fairly general assumptions, we show that in both cases a solution of the mean field game exists in feedback form and it induces approximate Nash equilibria for the N-player games when N is sufficiently large. This approximation result is established under non-degeneracy of the diffusion coefficient. The degenerate case is more delicate and might lead to counter-examples. The talk is based on joint works with Markus Fischer, Maddalena Ghio and Giulia Livieri.