Before revision:  We prove the existence of a Nash equilibrium and characterize the value functions of this differential game as the unique viscosity solutions of the corresponding Hamilton Jacobi Isaacs equations. Furthermore, optimal extraction and taxation policies that should be applied when the equilibrium is reached are derived .
After revision:  We prove the existence of a Nash equilibrium and characterize the value functions as well as the optimal extraction and taxation policies that should be applied when the equilibrium is reached are derived .