Master equation for Cournot mean field games of control with absorption

We establish the existence and uniqueness of a solution to master equation for mean field game controls with absorption. The arises as continuum limit dynamic exhaustible resources modeling Cournot competition between producers. proof relies on an analysis forward-backward system nonlocal Hamilton-Jacobi/Fokker-Planck equations Dirichlet boundary conditions. In particular, we new priori estimates prove that solutions are differentiable respect initial measure.