# Mean field games systems of first order

arXiv: https://arxiv.org/abs/1401.1789 · HTML: https://mlsanity.com/paper/1401.1789/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2014.

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

- [Learning Surrogate Potential Mean Field Games via Gaussian Processes: A Data-Driven Approach to Ill-Posed Inverse Problems](https://mlsanity.com/paper/2502.11506/) (2025)
- [Deep Learning for Mean Field Optimal Transport](https://mlsanity.com/paper/2302.14739/) (2023)

## Abstract (arXiv)

We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this solution as the minimizer of some optimal control of Hamilton-Jacobi and continuity equations. We also prove that this solution converges in the long time average to the solution of the associated ergodic problem.