  We characterize the shape of spatial externalities in a continuous time and
space differential game with transboundary pollution. We posit a realistic
spatiotemporal law of motion for pollution (diffusion and advection), and
tackle spatiotemporal non-cooperative (and cooperative) differential games.
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. We allow for a
rich set of geographic heterogeneities across states. We solve analytically the
induced non-cooperative differential game and characterize its long-term
spatial distributions. In particular, we prove that there exist a Perfect
Markov Equilibrium, unique among the class of the affine feedbacks. We further
provide with a full exploration of the free riding problem and the associated
border effect.
