A dynamic theory of spatial externalities
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.
Keywords
Cite
@article{arxiv.2112.10584,
title = {A dynamic theory of spatial externalities},
author = {Raouf Boucekkine and Giorgio Fabbri and Salvatore Federico and Fausto Gozzi},
journal= {arXiv preprint arXiv:2112.10584},
year = {2021}
}