A Cucker-Smale inspired deterministic mean field game with velocity interactions

TL;DR

This paper develops a mean field game model inspired by Cucker-Smale dynamics to analyze pedestrian movement, proving the existence of equilibrium and exploring its properties and regularity.

Contribution

It introduces a new deterministic mean field game model with velocity interactions, leveraging a variational approach to establish equilibrium existence and analyze its features.

Findings

Existence of equilibrium in the proposed model

Regularity properties of the equilibrium

Insights into velocity-based pedestrian interactions

Abstract

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.