What does a dynamic oligopoly maximize? The continuous time Markov case

We analyze the question of whether the outcome of an oligopoly exploiting a nonrenewable resource can be replicated by a related monopoly, within the framework of continuous time and Markov Perfect Nash Equilibrium. We establish necessary and sufficient conditions and find explicit solutions in some cases. Also, very simple models with externalities are shown which Nash equilibrium cannot be replicated in a monopoly.