Polluted River Problems and Games with a Permission Structure

Tinbergen Institute Discussion Paper 15-108/II

43 Pages Posted: 19 Sep 2015

See all articles by René van den Brink

René van den Brink

VU University Amsterdam - Department of Economics; Tinbergen Institute; Tinbergen Institute

Simin He

Shanghai University of Finance and Economics - School of Economics

Jia-Ping Huang

Vrije Universiteit Amsterdam, School of Business and Economics

Date Written: August 26, 2015

Abstract

Polluted rivers are harmful to human, animals and plants living along it. To reduce the harm, cleaning costs are generated. However, when the river passes through several different countries or regions, a relevant question is how should the costs be shared among the agents. Ni and Wang (2007) first consider this problem as cost sharing problems on a river network, shortly called polluted river problems. They consider rivers with one spring which was generalized by Dong, Ni, and Wang (2012) to rivers with multiple springs. They introduce and axiomatize three cost sharing methods: the Local Responsibility Sharing (LRS) method, the Upstream Equal Sharing (UES) method and the Downstream Equal Sharing (DES) method.

In this paper, we show that the UES and DES methods can also be obtained as the conjunctive permission value of an associated game with a permission structure, where the permission structure corresponds to the river structure and the game is determined by the cleaning costs. Then, we show that several axiomatizations of the conjunctive permission value also give axiomatizations of the UES and DES methods, of which one is comparable with the one from Dong, Ni, and Wang (2012). Besides, by applying another solution, the disjunctive permission value, to polluted river games with a permission structure we obtain a new cost allocation method for polluted river problems. We axiomatize this solution and compare it with the UES method.

Keywords: Polluted river, cost sharing, axiomatization, permission values

JEL Classification: C71, D61, D62

Suggested Citation

van den Brink, J.R. (René) and He, Simin and Huang, Jia-Ping, Polluted River Problems and Games with a Permission Structure (August 26, 2015). Tinbergen Institute Discussion Paper 15-108/II, Available at SSRN: https://ssrn.com/abstract=2657489 or http://dx.doi.org/10.2139/ssrn.2657489

J.R. (René) Van den Brink (Contact Author)

VU University Amsterdam - Department of Economics ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Simin He

Shanghai University of Finance and Economics - School of Economics ( email )

777 Guoding Road
Shanghai, 200433
China

Jia-Ping Huang

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

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