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Responsibility and sharing the cost of cleaning a polluted river

Panfei Sun (), Dongshuang Hou () and Hao Sun ()
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Panfei Sun: Northwestern Polytechnical University
Dongshuang Hou: Northwestern Polytechnical University
Hao Sun: Northwestern Polytechnical University

Mathematical Methods of Operations Research, 2019, vol. 89, issue 1, 143-156

Abstract: 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.

Keywords: Cost allocation; Local Responsibility Sharing; Upstream Equal Sharing; Axiomatization (search for similar items in EconPapers)
Date: 2019
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Handle: RePEc:spr:mathme:v:89:y:2019:i:1:d:10.1007_s00186-019-00658-w