The impact of pollution transmission networks in a transboundary pollution game

To explore transboundary pollution games with network externalities, this study develops a multi-region differential game which investigates the interaction and co-evolution of multiple pollution stocks across a continuous horizon. Pollution transmission networks are incorporated into the model via an adjacency matrix, detailing transmission paths of pollution across regions. Equilibrium strategies for emissions and investments in pollution control are obtained through a system of coupled differential equations. Our study demonstrates that these equilibrium strategies and the corresponding discounted net welfare of regions depend crucially on the structure of pollution transmission networks. The spectral properties of networks can effectively discern the evolutionary stability of equilibrium strategies. Through a numerical simulation of multiregional pollution dynamics, we also show that regions' motivation for pollution control decreases continuously as their influence in pollution transmission networks (i.e., network influence) increases; Nevertheless, an increase in a region's network influence can significantly reduce local pollution stocks in cycle networks but increase them in tree networks.