Calculus of Variations and Geometric Measure Theory

F. Santambrogio - W. Shim

A Cucker-Smale inspired deterministic Mean Field Game with velocity interactions

created by santambro on 15 Sep 2020
modified on 18 Jul 2021


Accepted Paper

Inserted: 15 sep 2020
Last Updated: 18 jul 2021

Journal: SIAM J. Contr. Opt.
Year: 2021


We introduce a mean field game model for pedestrians moving in a given domain and choosing their trajectories so as to minimize a cost including a penalization on the difference between their own velocity and that of the other agents they meet. We prove existence of an equilibrium in a Lagrangian setting by using its variational structure, and then study its properties and regularity.