Sharing a polluted river through environmental taxes

Abstract

n agents located along a river generate residues that then require cleaning to return the river to its natural state, which entails some cost. We propose several rules to distribute the total pollutant-cleaning cost among all the agents. We provide axiomatic characterizations using properties based on water taxes. Moreover, we prove that one of the rules coincides with the weighted Shapley value of a game associated with the problem.

A unified cooperative model for environmental costs in supply chains: the Shapley value for the linear case

“…This particular allocation can be called Upstream Equal Sharing (UES) cost allocation. Similarly, thanks to the result provided in Ni and Wang (2007) and Gómez-Rúa (2013), the game (N , C, ν 3 ) admits a Shapley value, i.e. x i i s 1 c s /(n − s + 1).…”

Two new classes of methods to share the cost of cleaning up a polluted river

“…The pollution cost-sharing game can be regarded as a compromise between the LRS game and the UES game, taking into account the local responsibility principle (implied by ATS theory (Godana 1985)) and the upstream responsibility principle (implied by the UTI theory (Kilgour and Dinar 1995)) in International Water Law. The ATS theory says that a country has absolute sovereignty over the area of any river basin on its territory, which can be interpreted as that the responsibility for the costs of cleaning river pollutants in a segment should be assigned to the agent located in that segment.…”

“…On the beneficial side, Ambec and Sprumont (2002) were the first to model the situation where a group of agents located along a river share its resources from a cooperative game-theoretic viewpoint, and studied how the water should be allocated among agents. They proposed the downstream incremental method in terms of the two main doctrines of Absolute Territorial Sovereignty (Godana 1985) and Unlimited Territorial Integrity (Kilgour and Dinar 1995) (for short, ATS and UTI, respectively) in international disputes. Ambec and Ehlers (2008) extended the model of sharing a river and considered the problem of efficiently sharing water from a river among a group of satiable agents.…”

Sharing the costs of cleaning a river: the Upstream Responsibility rule

“…Based on a different principle (the "polluter-pays" principle), Gómez-Rúa [9] defines water taxes according to regions' responsibilities for pollution and characterizes several cost allocation rules based on properties of those taxes. Other papers such as Gengenbach et al [7] and van der Laan and Moes [16] generalize the aforesaid model by allowing for satiable agents.…”