Sharing the costs of cleaning a river: the Upstream Responsibility rule

The cleaning up of waste present in transboundary rivers, which re- quires the cooperation of dierent authorities, is a problematic issue, espe- cially when responsibility for the discharge of the waste is not well-dened. Following Ni and Wang [12] we assume that a river is a segment divided into several regions from upstream to downstream. We show that when the transfer rate of the waste is unknown, the clean-up cost vector provides useful information for estimating some limits in regard to the responsi- bility of each region. We propose a cost allocation rule, the Upstream Responsibility rule, which takes into account these limits in distributing costs \fairly" and we provide an axiomatic characterization of this rule via certain properties based on basic ideas concerning the responsibility of regions.