In this talk I will present some new results on systems of PDE that appear in applications to markets of exhaustible resources. I will start by reviewing some of the literature on “extended mean field games” (or “mean field games of controls”) from recent years. As a particular example, I will discuss a model of exhaustible resource production considered by Guéant-Lasry-Lions and more recently by Chan-Sircar. Finally, I will present some of the latest theoretical results on existence, uniqueness, and regularity of solutions to models of this type.

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