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

arXiv: https://arxiv.org/abs/2009.07519 · HTML: https://mlsanity.com/paper/2009.07519/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2020.

## Built on by (most cited first, 2 of 2)

- [Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence](https://mlsanity.com/paper/2204.11924/) (2022)
- [Learning Distributed Equilibria in Linear-Quadratic Stochastic Differential Games: An α-Potential Approach](https://mlsanity.com/paper/2602.16555/) (2026)

## Abstract (arXiv)

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.