489

IGPM489.pdf February 2019 
TITLE 
Consistent mean field optimality conditions for interacting agent systems 
AUTHORS 
Michael Herty, Christian Ringhofer 
ABSTRACT 
We are interested in the derivation of optimality conditions for controlled interacting
agent systems. We establish the relation between mean field optimality conditions and the optimality
condition of the mean field control problem. This link is important for many recently published articles
on control strategies for agent based systems since it establishes the precise relation between multipliers
for the individual agents and the probability density distribution of the multipliers in the mean field
limit. The relation to different notions of differentiability are also shown. 
KEYWORDS 
Kinetic Equations, Particle Systems, Optimal Control, Meanfield Limits
