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arXiv · 2405.01812

Learning equilibria in Cournot mean field games of controls

Fabio Camilli·Mathieu Laurière·Qing Tang
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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.

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Fabio Camilli, Mathieu Laurière, Qing Tang. 2024-05-03. Learning equilibria in Cournot mean field games of controls. https://arxiv.org/abs/2405.01812

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