On the system of partial differential equations arising in mean field type control

TL;DR

This paper studies a coupled system of PDEs from mean field control problems, providing existence and uniqueness results, and compares mean field games with mean field type control through models and simulations.

Contribution

It introduces new existence and uniqueness results for PDE systems in mean field control and compares different mean field approaches with simple pedestrian models.

Findings

Existence and uniqueness results for the PDE system.

Numerical simulations comparing mean field games and control.

Insights into pedestrian motion modeling.

Abstract

We discuss the system of Fokker-Planck and Hamilton-Jacobi-Bellman equations arising from the finite horizon control of McKean-Vlasov dynamics. We give examples of existence and uniqueness results. Finally, we propose some simple models for the motion of pedestrians and report about numerical simulations in which we compare mean filed games and mean field type control.