Speaker: Daniel Lacker, Princeton University
ABSTRACT
Mean field game (MFG) theory generalizes models of interacting particle systems by replacing the particles with rational agents, making the theory applicable in economics and other social sciences. Intuitively, (stochastic differential) MFGs are infinite-population analogs of large-population stochastic differential games of a certain symmetric type, and a solution of the MFG is analogous to a Nash equilibrium. There are several known interpretations of MFG solutions, in terms of forward-backward systems of PDEs or McKean-Vlasov SDEs, but this talk will focus more on how to make rigorous sense of this mean field limit.
Under general assumptions on the data, we show that the set of "weak solutions" of the MFG equals precisely the set of possible limits (in distribution) of approximate Nash equilibria of the corresponding large-population games, as the number of agents tends to infinity. We elaborate on how certain forms of randomness can prevail in the limit which are well beyond the scope of the usual notion of MFG solution considered thus far in the literature.