Adjacent Downstream Compensation Method of Sharing Polluted Rivers
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Adjacent Downstream Compensation Method of Sharing Polluted Rivers Dongshuang Hou1 · Qianqian Kong1 · Xia Zhang1 · Hao Sun1 Accepted: 27 October 2020 © Springer Nature B.V. 2020
Abstract To clean up the pollutants in cross-boundary rivers needs the collaborative actions among different agents involved. In our paper, we deal with the river pollution problem in a cooperative situation. We first introduce the adjacent downstream compensation method by considering the bargaining behavior between any two neighbour agents, which reconciles two famous doctrines in the international disputes, i.e., the Absolute Territorial Sovereignty theory and the Unlimited Territorial Integrity theory. Then we prove the coincidence of the adjacent downstream compensation method and the Shapley value of the corresponding responsibility game. By studying the concavity of the river pollution cost sharing game, we illustrate the stability of the adjacent downstream compensation method. Keywords Game theory · Cost allocation · Polluted river · Adjacent downstream compensation method · Shapley value Mathematics Subject Classification 91A12 · C71
* Dongshuang Hou [email protected] Qianqian Kong [email protected] Xia Zhang [email protected] Hao Sun [email protected] 1
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, People’s Republic of China
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1 Introduction The polluted water problem may lead to the ecological unbalance of a river as well as the natural disasters (Ambec and Sprumont 2002; Ambec and Ehlers 2008). To control the water pollution, the corresponding pollution cleanup cost is incurred and should be split among the agents located along the rivers. Without loss of generality, we establish a relationship between the river and the agent such that the agent located along the river has the same denoted number with this river. We consider the pollution cleanup cost allocation among the agents. In the case that a river flows through only one region (country), this region (country) has to undertake the whole cleanup cost without doubt. While for the case when rivers flow across different regions (countries), it refers to co-cleaning up pollution issues. Plenty of literature concentrating on river pollution allocation issues by applying game theory approach can be found. Examples include Brink et al. (2018), Dong et al. (2012), Ni and Wang (2007) and Sun et al. (2019). Although the given cost allocations in the above literature are very valuable, they ignore two important factors. One is that the river basin itself has certain discharging pollution function. This idea can be traced back to Vanderpoorten (1999), which stated the hydrophyte filter bed was able to improve the water quality. In view of this, when allocating the pollution cleanup costs, the discharging pollution function should be considered. Several other papers have applied this idea by introducing the so-called transferred rate when conducting on the sharing a polluted river, e.g.,
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