# Schauder Estimates for a Class of Potential Mean Field Games of Controls

arXiv: https://arxiv.org/abs/1902.05461 · HTML: https://mlsanity.com/paper/1902.05461/

## Key facts

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

## 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)

An existence result for a class of mean field games of controls is provided. In the considered model, the cost functional to be minimized by each agent involves a price depending at a given time on the controls of all agents and a congestion term. The existence of a classical solution is demonstrated with the Leray-Schauder theorem; the proof relies in particular on a priori bounds for the solution, which are obtained with the help of a potential formulation of the problem.