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arXiv · 2112.10584

A dynamic theory of spatial externalities

Raouf Boucekkine·Giorgio Fabbri·Salvatore Federico·Fausto Gozzi
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Abstract

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.

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Raouf Boucekkine, Giorgio Fabbri, Salvatore Federico, Fausto Gozzi. 2021-12-20. A dynamic theory of spatial externalities. https://arxiv.org/abs/2112.10584

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