# On mean field games models for exhaustible commodities trade

arXiv: https://arxiv.org/abs/1807.10344 · HTML: https://mlsanity.com/paper/1807.10344/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2018.

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

- [Deep Learning for Principal-Agent Mean Field Games](https://mlsanity.com/paper/2110.01127/) (2021)

## Abstract (arXiv)

We investigate a mean field game model for the production of exhaustible resources. In this model, firms produce comparable goods, strategically set their production rate in order to maximise profit, and leave the market as soon as they deplete their capacities. We examine the related Mean Field Game system and prove well-posedness for initial measure data by deriving suitable a priori estimates. Then, we show that feedback strategies which are computed from the Mean Field Game system provide varepsilon-Nash equilibria to the corresponding N-Player Cournot game, for large values of N. This is done by showing tightness of the empirical process in the Skorokhod rm M 1 topology, which is defined for distribution-valued processes.