Mean Field Game

Mean field games (MFGs) study strategic decision making in large populations where the individual players with each other and each individual is effected only by certain averaged quantities of all the other individuals. MFGs are studied by taking the limit of infinitely many individual players and replacing individual interactions by an average or effective interaction.

The mean-field refers to representing the behavior of a large number of agents by their population density function. This setting connects deeply with optimal transport theory, Nelson's stochastic mechanics (Schrodinger equation, Schrodinger bridge problem), partial differential equations, optimization, probability and statistics with applications in machine learning problems.

Our MFG research is supported by AFOSR MURI FA9550-18-1-0502 “Innovations in Mean-Field Game Theory for Scalable Computation and Diverse Applications.”