Title: Mean-field games: the linear programming approach

Abstract: We will review the linear programming approach to mean-field games, developed by the author in a series of papers. Mean-field games are games with a large number of identical small agents and symmetric interactions, which have found many applications in finance and economics. The linear programming approach is a relaxation technique, which allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We will present an application of the approach to a model of energy markets and discuss the « linear programming fictitious play » algorithm for approximating the equilibrium.