Mean-field game

Summary

A mean-field game is a differential game with a very large number of small, identical players. Each player reacts only to the distribution of all the others. In the limit of infinitely many players, a Nash equilibrium is described by a coupled system of two partial differential equations. A Hamilton–Jacobi–Bellman equation backward in time gives the optimal strategy of one player. A Fokker–Planck equation forward in time gives the evolution of the distribution of players. The theory was introduced independently by Jean-Michel Lasry and Pierre-Louis Lions and by Minyi Huang, Roland Malhamé and Peter Caines.