# Convergence of large population games to mean field games with interaction through the controls

arXiv: https://arxiv.org/abs/2004.08351 · HTML: https://mlsanity.com/paper/2004.08351/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2020.

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

- [Reinforcement Learning for Mean Field Games, with Applications to Economics](https://mlsanity.com/paper/2106.13755/) (2021)

## Abstract (arXiv)

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence of finite-player games to the asymptotic mean field game. Our approach is based on the concept of propagation of chaos for forward and backward weakly interacting particles which we investigate by stochastic analysis methods, and which appear to be of independent interest. These propagation of chaos arguments allow to derive moment and concentration bounds for the convergence of Nash equilibria.