## Abstract

Consider n firms (agents) located at a river, indexed by 1 , ⋯ , n from upstream to downstream. The pollution generated by these firms induce cleaning costs c _{1} , ⋯ , 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 , ⋯ , 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.

Original language | English |
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Pages (from-to) | 143-156 |

Number of pages | 14 |

Journal | Mathematical methods of operations research |

Volume | 89 |

Issue number | 1 |

DOIs | |

Publication status | Published - 19 Feb 2019 |

## Keywords

- Axiomatization
- Cost allocation
- Local Responsibility Sharing
- Upstream Equal Sharing