496 IGPM496.pdf        October 2019
TITLE Microscopic Derivation of Mean Field Game Models
AUTHORS Martin Frank, Michael Herty, Torsten Trimborn
ABSTRACT Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade [27]. In this work, we derive mean field game partial differential equation systems from deterministic microscopic agent dynamics. The dynamics are given by a particular class of ordinary differential equations, for which an optimal strategy can be computed [10]. We use the concept of Nash equilibria and apply the dynamic programming principle to derive the mean field limit equations and we study the scaling behavior of the system as the number of agents tends to infinity and find several mean field game limits. Especially we avoid in our derivation the notion of measure derivatives. Novel scales are motivated by an example of an agent-based financial market model.
KEYWORDS mean field game, di fferential game, Nash equilibria, microscopic derivation, dynamic programming principle, scales, mean fi eld limit, Levy-Levy-Solomon model