Mathematical Methods of Operations Research

, Volume 89, Issue 1, pp 143–156 | Cite as

Responsibility and sharing the cost of cleaning a polluted river

  • Panfei Sun
  • Dongshuang HouEmail author
  • Hao Sun
Original Article


Consider n firms (agents) located at a river, indexed by \(1, \dots , n\) from upstream to downstream. The pollution generated by these firms induce cleaning costs \(c_1, \dots , c_n\), where \(c_i\) 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 \(c_i\) to the corresponding firm i. The second distributes each \(c_i\) equally among firms \(1, \dots , i\). 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.


Cost allocation Local Responsibility Sharing Upstream Equal Sharing Axiomatization 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Applied MathematicsNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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