Equilibrium strategies in a multiregional transboundary pollution differential game with spatially distributed controls

TL;DR

This paper models a multiregional transboundary pollution problem using a spatially distributed differential game, analytically characterizing equilibrium strategies and highlighting the importance of geographical relationships in emission decisions.

Contribution

It introduces an analytical framework for equilibrium strategies in a spatially distributed pollution game, emphasizing the role of geography in strategic emission choices.

Findings

Equilibrium emission levels depend on geographical relationships.

Spatial considerations significantly influence optimal strategies.

The model demonstrates the importance of geography in pollution control.

Abstract

We analyze a differential game with spatially distributed controls to study a multiregional transboundary pollution problem. The dynamics of the state variable (pollution stock) is defined by a two dimensional parabolic partial differential equation. The control variables (emissions) are spatially distributed variables. The model allows for a, possibly large, number of agents with predetermined geographical relationships. For a special functional form previously used in the literature of transboundary pollution dynamic games we analytically characterize the feedback Nash equilibrium. We show that at the equilibrium both the level and the location of emissions of each region depend on the particular geographical relationship among agents. We prove that, even in a simplified model, the geographical considerations can modify the players' optimal strategies and therefore, the spatial aspects of the model should not be overlooked.