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Responsibility and sharing the cost of cleaning a polluted river

Author

Listed:
  • Panfei Sun

    (Northwestern Polytechnical University
    University of Twente)

  • Dongshuang Hou

    (Northwestern Polytechnical University)

  • Hao Sun

    (Northwestern Polytechnical University)

Abstract

Consider n firms (agents) located at a river, indexed by $$1, \dots , n$$ 1 , ⋯ , n from upstream to downstream. The pollution generated by these firms induce cleaning costs $$c_1, \dots , c_n$$ c 1 , ⋯ , c n , where $$c_i$$ c i is the cost for cleaning the water in region i (according to the local environmental standards). The corresponding cost allocation problem is highly interesting both in theory and practice. Among the most prominent allocation schemes are the so-called Local Responsibility and Upstream Equal Sharing. The first one allocates simply each local cost $$c_i$$ c i to the corresponding firm i. The second distributes each $$c_i$$ c i equally among firms $$1, \dots , i$$ 1 , ⋯ , i . We propose and characterize a dynamic scheme which, given a particular order of arrival, allocates the current total cost among the firms that have arrived so far. The corresponding expected allocation (w.r.t. a random arrival order) turns out to be a convex combination of the two schemes above.

Suggested Citation

  • Panfei Sun & Dongshuang Hou & Hao Sun, 2019. "Responsibility and sharing the cost of cleaning a polluted river," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 143-156, February.
    • Handle: RePEc:spr:mathme:v:89:y:2019:i:1:d:10.1007_s00186-019-00658-w
    DOI: 10.1007/s00186-019-00658-w
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    References listed on IDEAS

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    1. Alcalde-Unzu, Jorge & Gómez-Rúa, María & Molis, Elena, 2015. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Games and Economic Behavior, Elsevier, vol. 90(C), pages 134-150.
    2. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2012. "Fair agreements for sharing international rivers with multiple springs and externalities," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 388-403.
    3. Marcin Malawski, 2013. "“Procedural” values for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 305-324, February.
    4. Panfei Sun & Dongshuang Hou & Hao Sun & Theo Driessen, 2017. "Optimization Implementation and Characterization of the Equal Allocation of Nonseparable Costs Value," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 336-352, April.
    5. Anna Khmelnitskaya, 2010. "Values for rooted-tree and sink-tree digraph games and sharing a river," Theory and Decision, Springer, vol. 69(4), pages 657-669, October.
    6. Barret, Scott & DEC, 1994. "Conflict and cooperation in managing international water resources," Policy Research Working Paper Series 1303, The World Bank.
    7. van den Brink, René & He, Simin & Huang, Jia-Ping, 2018. "Polluted river problems and games with a permission structure," Games and Economic Behavior, Elsevier, vol. 108(C), pages 182-205.
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    Cited by:

    1. Dongshuang Hou & Aymeric Lardon & Panfei Sun & Genjiu Xu, 2019. "Sharing a Polluted River under Waste Flow Control," GREDEG Working Papers 2019-23, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    2. Wenzhong Li & Genjiu Xu & Rene van den Brink, 2021. "Sharing the cost of cleaning up a polluted river," Tinbergen Institute Discussion Papers 21-028/II, Tinbergen Institute.
    3. Jorge Alcalde-Unzu & María Gómez-Rúa & Elena Molis, 2021. "Allocating the costs of cleaning a river: expected responsibility versus median responsibility," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 185-214, March.
    4. Jens Gudmundsson & Jens Leth Hougaard, 2021. "River pollution abatement: Decentralized solutions and smart contracts," IFRO Working Paper 2021/07, University of Copenhagen, Department of Food and Resource Economics, revised Oct 2021.
    5. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2023. "A linear model for freight transportation," MPRA Paper 119301, University Library of Munich, Germany.
    6. Dongshuang Hou & Qianqian Kong & Xia Zhang & Hao Sun, 2021. "Adjacent Downstream Compensation Method of Sharing Polluted Rivers," Group Decision and Negotiation, Springer, vol. 30(1), pages 251-265, February.
    7. Wenzhong Li & Genjiu Xu & René van den Brink, 2023. "Two new classes of methods to share the cost of cleaning up a polluted river," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(1), pages 35-59, July.
    8. Jens Gudmundsson & Jens Leth Hougaard & Chiu Yu Ko, 2020. "Sharing sequentially triggered losses," IFRO Working Paper 2020/05, University of Copenhagen, Department of Food and Resource Economics.
    9. Abraham, Anand & Ramachandran, Parthasarathy, 2020. "A solution for the flood cost sharing problem," Economics Letters, Elsevier, vol. 189(C).

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