A dynamic theory of spatial externalities

TL;DR

This paper develops a continuous-time, spatially explicit differential game model to analyze transboundary pollution, characterizing equilibrium pollution distributions and exploring free riding and border effects in a heterogeneous geographic setting.

Contribution

It introduces a novel analytical framework for spatial externalities in pollution management, incorporating realistic diffusion-advection dynamics and geographic heterogeneity.

Findings

Existence and uniqueness of a Perfect Markov Equilibrium.

Analytical characterization of long-term spatial pollution distribution.

Insights into free riding and border effects in transboundary pollution.

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.