489 IGPM489.pdf        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