A Dynamic Theory Of Spatial Externalities

This work targets the class of spatiotemporal problems with free riding under natural (pollution, epidemics...etc) diffusion and spatial externalities. Such a class brings to study a family of differential games in continuous time and space. In the fundamental pollution free riding problem we develop a strategy to solve completely the associated game contributing to the associated debate on environmental federalism. We depart from the preexisting literature in several respects. First, instead of assuming ad hoc pollution diffusion schemes across space, we consider a realistic spatiotemporal law of motion for pollution (diffusion and advection). Second, we tackle spatiotemporal non-cooperative (and cooperative) differential games instead of static games in the related literature. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. Third, we allow for a rich set of geographic heterogeneities across states while the literature assumes identical states. We solve analytically the induced non-cooperative differential game under decentralization and fully characterize the resulting long-term spatial distributions. In particular, we prove that there exist a Perfect Markov Equilibrium, unique among the class of the a ne feedbacks. We further provide with full exploration of the free riding problem, reflected in the so-called border effects. Finally, we explore how geographic discrepancies (the most elementary being the asymmetry of players) affect the shape of the border effects. We check in particular that our model is consistent with the set of stylized facts put forward by the related empirical literature.