Sharing a River with Downstream Externalities

Sarina Steinmann,Ralph Winkler

doi:10.3390/g10020023

Sarina Steinmann, Ralph Winkler

Open Access

https://doi.org/10.3390/g10020023

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Abstract

We consider the problem of efficient emission abatement in a multi polluter setting, where agents are located along a river in which net emissions accumulate and induce negative externalities to downstream riparians. Assuming a cooperative transferable utility game, we seek welfare distributions that satisfy all agents’ participation constraints and, in addition, a fairness constraint implying that no coalition of agents should be better off than it were if all non-members of the coalition would not pollute the river at all. We show that the downstream incremental distribution, as introduced by Ambec and Sprumont (2002), is the only welfare distribution satisfying both constraints. In addition, we show that this result holds true for numerous extensions of our model.

Highlights

Industries and cities all around the world have historically been concentrated along rivers, since rivers provide means of transportation, food production, energy generation and drinking water.Because of this intensive utilization, many rivers and streams have been and still are being heavily polluted
If upstream polluters and downstream riparians belong to different jurisdictions, polluters may have little incentive to abate their emissions, because they cannot be held liable for the pollution damage caused in other jurisdictions
We show that the downstream incremental distribution, as introduced by Ambec and Sprumont [1], is the only distribution simultaneously satisfying the non-cooperative core upper cost bounds and the aspiration lower cost bounds

Summary

Introduction

Industries and cities all around the world have historically been concentrated along rivers, since rivers provide means of transportation, food production, energy generation and drinking water. Interpreting the river sharing problem as a line-graph game, Van den Brink et al [2] derive four different efficient solutions including the downstream incremental distribution by imposing various properties with respect to deleting edges of the line-graph They do not address fairness issues and consider non-satiable agents. [9] the results are generalized to agents exhibiting satiation in water consumption They show that the downstream incremental distribution is the only welfare distribution satisfying the non-cooperative core lower bounds and the aspiration welfare upper bounds. While water consumption is a purely private good, emission abatement exhibits public good characteristics, as it imposes positive externalities on all downstream agents These additional externalities impose non-trivial complications for proving that the downstream incremental distribution satisfies the non-cooperative cost upper bounds and the aspiration cost lower bounds in the formulation of our river pollution model. In contrast, focus on the derivation of the unique sharing rule that satisfies the two axioms of lower and upper cost bounds

A River Sharing Model with Downstream Pollution Externalities

Coalitions and Cost Upper Bounds

Cost Lower Bounds

The Downstream Incremental Distribution

Discussion and Extensions

Conclusions