Learning equilibria in Cournot mean field games of controls

TL;DR

This paper studies Cournot mean field games of controls, proving solution uniqueness, convergence of a learning algorithm, and providing numerical methods with examples to analyze the impact of parameters.

Contribution

It introduces a new convergence proof for a learning algorithm in Cournot mean field games of controls and develops a numerical discretization method.

Findings

Proved uniqueness of solutions under general price function assumptions.

Established convergence of the proposed learning algorithm.

Provided numerical examples illustrating parameter impacts.

Abstract

We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the solution under general assumptions on the price function. Then, we prove convergence of a learning algorithm which gives existence of a solution to the mean field games system. The learning algorithm is implemented with a suitable finite difference discretization to get a numerical method to the solution. We supplement our theoretical analysis with several numerical examples and illustrate the impacts of model parameters.