Daniel Lacker: Mean field games and the convergence problem

This talk is a brief introduction to mean field games, with a focus on the probabilistic limit theory. Mean field game theory describes continuum limits of large-population games. Many models in this framework arise as competitive extensions of classical models of interacting particle systems, where the particles are now "controlled state processes" with application-specific interpretation, such as position, income, wealth, etc.

The coupled optimization problems faced by each process are typically resolved by Nash equilibrium, and there is a large and growing literature on solvability problems for the continuum models (both theoretical and computational). On the other hand, far less is known on how to rigorously pass from a finite population to a continuum.

The basic question is: Given for each \(n\) a Nash equilibrium for the \(n\)-player game, in what sense do the equilibria converge as \(n\rightarrow\infty\)? The talk will discuss recent progress on this surprisingly delicate question.