We consider a finite-horizon two-player differential game where the players face a common terminal environmental constraint. Our aim is to verify whether the result obtained in a static context, namely, that the Pareto-optimal cooperative solution can be attained as a normalized noncooperative Rosen equilibrium, can be generalized to a dynamic setting. We show that this is not the case. However, we provide a taxation mechanism of players' emissions that forces them to implement the less-polluting cooperative strategies.