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 Unlimited 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 (Games Econ Behav 60:176–186, 2007) 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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References
Ambec S (2008) Sharing a resource with concave benefits. Soc Choice Welf 31: 1–13
Ambec S, Ehlers L (2008) Sharing a river among satiable agents. Games Econ Behav 64(1): 35–50
Ambec S, Ehlers L et al (2008) Cooperation and equity in the river sharing problem. In: Dinar A (ed) Game theory and policy making in natural resources and the environment. Routledge, London
Ambec S, Sprumont Y (2002) Sharing a River. J Econ Theory 107: 453–462
Ansink E, Ruijs A (2008) Climate change and the stability of water allocation agreements. Environ Resour Econ 41: 249–266
Barrett S (1994) Conflict and cooperation in managing international water resources, Working Paper 1303, World Bank, Washington
Coase R (1960) The problem of social cost. J Law Econ 1: 1–14
Godana B (1985) Africa’s shared water resources. France Printer, London
Hung M-F, Shaw D (2005) A trading-ratio system for trading water pollution discharge permits. J Environ Econ Manag 49: 83–102
Kilgour M, Dinar A (1996) Are stable agreements for sharing international river waters now possible? Working Paper 1474, World Bank, Washington
Kilgour M, Dinar A (2001) Flexible water sharing within an international river basin. Environ Resour Econ 18: 43–60
Littlechild S, Owen G (1973) A simple expression for the Shapley value in a special case. Manag Sci 20: 370–372
Littlechild S, Thompson G (1977) Aircraft landing fees: a game theoretic approach. Bell J Econ 8: 186–204
Marchiori C (2010) Concern for fairness and incentives in water negotiations. Environ Resour Econ 45: 553–571
Moulin H (2002) Axiomatic cost and surplus sharing. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 1. North-Holland, Amsterdam
Moulin H (2011) Cost sharing in networks: some open questions. Working paper, Rice University
Ni D, Wang Y (2007) Sharing a polluted river. Games Econ Behav 60: 176–186
Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307–317
Shapley LS (1971) Core of convex games. Int J Game Theory 1: 11–26
Van den Brink JR, Gilles RP (1996) Axiomatizations of the conjunctive permission value for games with permission structures. Games Econ Behav 12: 113–126
Wang Y (2011) Trading water along a river. Math Soc Sci 61: 124–130
Weber ML (2001) Markets for water rights under environmental constraints. J Environ Econ Manag 42: 53–64
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We thank the two anonymous referees and the associate editor Hassan Benchekroun for their very helpful comments and suggestions that improve greatly our paper. We are grateful to Meidan Sun for her assistance in Sect. 3.4 of the paper. Ni would like to acknowledge the financial support from the Key Project of the Natural Sciences Foundation (NSF) of China (Grant # 70932005), the Regular Project of the Natural Sciences Foundation (NSF) of China (Grant # 70702025), the Program for the New Century Excellent Talents in Universities (Grant # NCET-11-0064) as well as the UESTC funds for Junior Research Chairs. Wang would like to thank Peter Townley, Sang-Chul Suh, and Ronald Meng for the comments and suggestions. Wang’s research was supported by the SSHRC of Canada under grant # 410-2005-0620.
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Dong, B., Ni, D. & Wang, Y. Sharing a Polluted River Network. Environ Resource Econ 53, 367–387 (2012). https://doi.org/10.1007/s10640-012-9566-2
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DOI: https://doi.org/10.1007/s10640-012-9566-2