We analyze a transboundary pollution differential game where, in addition to the standard temporal dimension, a spatial dimension is introduced capturing the geographical aspects. The spatio-temporal dynamics of the pollutant stock is described by a parabolic partial differential equation. Using aggregate variables we analytically characterize the feedback Nash equilibrium of a discrete-space model. As the parameter describing pollution diffusion grows, 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, compatible with greater long-run welfares. In the cooperative framework the only decision-maker still makes spatially strategic decisions.
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