Optimal coarse correlated equilibria in mean field games
Abstract
We will consider coarse correlated equilibria (CCE) in continuous time mean field games. CCEs are generalizations of Nash equilibria, when a moderator (correlation device) recommend strategies to the players that are not convenient to unilaterally reject. We will first address existence and approximations results when the number of players goes to infinity. Second, we will provide a linear programming approach through the notion of relaxed strategies in the same spirit as the works by Kurtz and Stockbridge, which have been recently extended to mean field games in several papers by Bouveret, Dumitrescu, Leutscher and Tankov. Within such a linear programming setting and under some regularity assumptions, we will show existence of an optimal CCE with respect to a fixed criterion for the moderator. Finally, we will propose an equivalent Lagrangian formulation and a primal-dual algorithm to compute an optimal CCE numerically. This talk is based on joint papers with F. Cannerozzi, F. Cartellier, M. Fischer and I. Tzouanas.
About the speaker
Luciano Campi is currently Full Professor of Probability and Mathematical Statistics at the Department of Mathematics "Federigo Enriques", University of Milan. His recent research focuses on stochastic control, stochastic differential games, mean field games, and their applications to energy markets. Before joining the University of Milan, he held academic positions at the London School of Economics, University Paris 13, and University Paris Dauphine. He earned his PhD in Mathematics from the University of Paris 6 and in Computational Mathematics from the University of Padua. Luciano Campi is an Associate Editor for the IMA Journal of Applied Mathematics and Decisions in Economics and Finance.