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.
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This work is supported by China Scholarship Council (No. 201706290159) and National Natural Science Foundation of China (Nos. 71571143, 71871180 and 71601156). And we also appreciate the help of Dr. W. Kern and the anonymous reviewers, who has given us some constructive suggestions.
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Sun, P., Hou, D. & Sun, H. Responsibility and sharing the cost of cleaning a polluted river. Math Meth Oper Res 89, 143–156 (2019). https://doi.org/10.1007/s00186-019-00658-w
- Cost allocation
- Local Responsibility Sharing
- Upstream Equal Sharing