The paper studies the relationships between two countries in a differential game setting where the control of each country is its emittance of pollutants. Each country wants to maximize its own welfare. The correspondence mathematical model consists of a one-dimensional differential equation in which the state represents the ``world wide'' stock of pollution. This state is influenced by the two controls. The problem statement is completed with two welfare functions, being the infinite horizon integration of a discounted instantaneous welfare. This instantaneous welfare is assumed to be a separable function of the control and the state, with some concavity restrictions on the shape. The paper considers three types of equilibria: cooperation, open-loop Nash and open-loop Stackelberg. Qualitative properties of the corresponding solutions are derived analytically (where the adjoint variable or the shadow price is used) and compared. Interpretations in terms of pollution, emission levels are given. Since the terminal time equals infinity, stability properties of the equilibrium solution are also investigated. It turns out that in the case of the Stackelberg equilibrium, bifurcations and limit cycles can occur depending on some specific parameters (such as the discount factor) defining the problem.