# On the asymptotic nature of first order mean field games

arXiv: https://arxiv.org/abs/1903.03602 · HTML: https://mlsanity.com/paper/1903.03602/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2019.

## Built on by (most cited first, 1 of 1)

- [Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games](https://mlsanity.com/paper/2505.22781/) (2025)

## Abstract (arXiv)

For a class of finite horizon first order mean field games and associated N-player games, we give a simple proof of convergence of symmetric N-player Nash equilibria in distributed open-loop strategies to solutions of the mean field game in Lagrangian form. Lagrangian solutions are then connected with those determined by the usual mean field game system of two coupled first order PDEs, and convergence of Nash equilibria in distributed Markov strategies is established.