  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.
