Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games

We analyze a transboundary pollution differential game where, in addition to the standard temporal dimension, a spatial dimension is introduced to capture the geographical relationships among regions. Each region behaves strategically and maximizes its welfare net of environmental damage caused by the pollutant stock. The emission-output ratio is reduced by investment in region specific clean technology which evolves over time. The spatio-temporal dynamics of the pollutant stock is described by a parabolic partial differential equation. Using aggregate variables we study the feedback Nash equilibrium of a discrete-space model which could be seen as a space discretization of the continuous-space model. The discrete-space model presents the three main features of the original formulation: the model is truly dynamic; the agents behave strategically; and the model incorporates spatial aspects. For special functional forms previously used in the literature we analytically characterize the feedback Nash equilibrium and evaluate the impact of the introduction of the spatial dimension in the economic-environmental model. We show that our spatial model is a generalization of the model that disregards the spatial aspects. We analytically show that as the parameter describing how pollution diffuses among regions tends to infinity the equilibrium policies converge to those in the non-spatial setting. In the non-cooperative framework the spatially non-myopic behavior prescribes lower equilibrium emission rates, and consequently a lower global pollution stock. This is compatible with greater long-run welfares. In the cooperative framework, although the strategic interaction among the players does not exist, the only decision-maker still makes spatially strategic decisions.