Games and Economic Behavior 60 (2007) 176–186
Sharing a polluted river
, Yuntong Wang
School of Management, University of Electronic Science and Technology of China, Chengdu, Sichuan,
PR China 610054
Department of Economics, University of Windsor, Windsor, ON, Canada N9B 3P4
Received 13 February 2006
Available online 16 November 2006
A river carries pollutants to people living along it if it is polluted. To make the water in the river clean,
some costs are incurred. This poses a question of how to split the costs of cleaning the whole river among
the agents located along it. To answer this question, we resort to the two main advocated doctrines in
international disputes: the theory of Absolute Territorial Sovereignty (ATS) and the theory of Unlimited
Territorial Integrity (UTI). Applying these two doctrines, we accordingly propose two methods: the Local
Responsibility Sharing (LRS) method and the Upstream Equal Sharing (UES) method. For each method, we
provide an axiomatic characterization. Interestingly, both the LRS method and the UES method coincide
with the Shapley value solutions to the corresponding (cost) games that are naturally induced according to
the ATS and the UTI doctrines respectively.
2006 Elsevier Inc. All rights reserved.
JEL classiﬁcation: C71; D61; D62
Keywords: Externality; Fair allocation of pollution costs; Shapley value
There are 148 rivers in the world ﬂowing through two countries, 30 through three, 9 through
four and 13 through ﬁve or more (see Ambec and Sprumont, 2002; Barret, 1994). Transborder
rivers provide people in different countries with water resources, but they also bring pollutants
Corresponding author. Fax: +1(519) 973-7096.
E-mail address: firstname.lastname@example.org (Y. Wang).
Debing Ni is a visiting scholar at the Department of Economics, University of Windsor, from March 2005 to February
0899-8256/$ – see front matter © 2006 Elsevier Inc. All rights reserved.