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Sharing a polluted river network

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  • Dong, Baomin
  • Ni, Debing
  • Wang, Yuntong

Abstract

A polluted river network is populated with agents (e.g., firms, villages, municipalities, or countries) located upstream and downstream. This river network must be cleaned, the costs of which must be shared among the agents. We model this problem as a cost sharing problem on a tree network. Based on the two theories in international disputes, namely the Absolute Territorial Sovereignty (ATS) and the Unlimitted Territorial Integrity (UTI), we propose three different cost sharing methods for the problem. They are the Local Responsibility Sharing (LRS), the Upstream Equal Sharing (UES), and the Downstream Equal Sharing (DES), respectively. The LRS and the UES generalize Ni and Wang ("Sharing a polluted river", Games Econ. Behav., 60 (2007), 176-186) but the DES is new. The DES is based on a new interpretation of the UTI. We provide axiomatic characterizations for the three methods. We also show that they coincide with the Shapley values of the three different games that can be defined for the problem. Moreover, we show that they are in the cores of the three games, respectively. Our methods can shed light on pollution abatement of a river network with multiple sovereignties.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 38839.

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Date of creation: 01 Apr 2012
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Handle: RePEc:pra:mprapa:38839

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Keywords: River network; Water pollution; Cost sharing; the Shapley value;

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  1. Hung, Ming-Feng & Shaw, Daigee, 2005. "A trading-ratio system for trading water pollution discharge permits," Journal of Environmental Economics and Management, Elsevier, vol. 49(1), pages 83-102, January.
  2. Aadland, David & Kolpin, Van, 1998. "Shared irrigation costs: An empirical and axiomatic analysis," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 203-218, March.
  3. Weber, Marian L., 2001. "Markets for Water Rights under Environmental Constraints," Journal of Environmental Economics and Management, Elsevier, vol. 42(1), pages 53-64, July.
  4. D. Kilgour & Ariel Dinar, 2001. "Flexible Water Sharing within an International River Basin," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 18(1), pages 43-60, January.
  5. Wang, Yuntong, 2011. "Trading water along a river," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 124-130, March.
  6. Erik Ansink & Arjan Ruijs, 2008. "Climate Change and the Stability of Water Allocation Agreements," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 41(2), pages 249-266, October.
  7. Ambec, S. & Ehlers, L., 2007. "Cooperation and equity in the river sharing problem," Working Papers 200705, Grenoble Applied Economics Laboratory (GAEL).
  8. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
  9. S.C. Littlechild & G.F. Thompson, 1977. "Aircraft Landing Fees: A Game Theory Approach," Bell Journal of Economics, The RAND Corporation, vol. 8(1), pages 186-204, Spring.
  10. Carmen Marchiori, 2010. "Concern for Fairness and Incentives in Water Negotiations," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 45(4), pages 553-571, April.
  11. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
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Cited by:
  1. Rene van den Brink & Jean-Jacques Herings & Gerard van der Laan & Dolf Talman, 2012. "The Average Tree Permission Value for Games with a Permission Tree," Tinbergen Institute Discussion Papers 13-023/II, Tinbergen Institute.

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