A dynamic theory of spatial externalities

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....

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Bibliographic Details
Published in:Games and economic behavior 2022-03, Vol.132, p.133-165
Main Authors: Boucekkine, Raouf, Fabbri, Giorgio, Federico, Salvatore, Gozzi, Fausto
Format: Article
Language:English
Subjects:
Differential games in continuous time and space
Economics and Finance
Environmental federalism
Humanities and Social Sciences
Infinite dimensional optimal control problems
Spatial diffusion
Spatial externalities
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Summary: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.
ISSN:0899-8256
1090-2473
DOI:10.1016/j.geb.2021.12.002