Applied Analysis and Dynamical Systems
Diogo Gomes, CEMSE Division, King Abdullah University of Science and Technology
Mean-field games models
The mean-field game framework was developed to study systems with an infinite number of rational agents in competition, which arise in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this talk we present a brief survey of various mean-field models as well as recent results and techniques. We start by discussing reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton–Jacobi equation and a transport or Fokker–Planck equation. We present in detail various examples, including extensions to population dynamics models. We will end the talk with a brief discussion of finite state mean-field games and the numerical analysis of such models.