496

RWTH Publication No: 772133 2019 IGPM496.pdf 
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 agentbased
financial market model. 
KEYWORDS 
mean field game, differential game, Nash equilibria, microscopic derivation, dynamic programming principle, scales, mean field limit, LevyLevySolomon model
