We consider the problem of cleaning a transboundary river, proposed by Ni and Wang (Games Econ Behav 60:176–186, 2007). A river is modeled as a segment divided into subsegments, each occupied by one region, from upstream to downstream. The waste is transferred from one region to the next at some rate. Since this transfer rate may be unknown, the social planner could have uncertainty over each region’s responsibility. Two natural candidates to distribute the costs in this setting would be the method that assigns to each region its expected responsibility and the one that assigns to each region its median responsibility. We show that the latter is equivalent to the Upstream Responsibility method (Alcalde-Unzu et al. in Games Econ Behav 90:134–150, 2015) and the former is a new method that we call Expected Responsibility. We compare both solutions and analyze them in terms of a new property of monotonicity.

中文翻译：

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分配清理河流的成本：预期责任与中间责任

我们考虑了 Ni 和 Wang (Games Econ Behav 60:176–186, 2007) 提出的清理跨界河流的问题。一条河流被建模为从上游到下游分为多个子段的段，每个子段由一个区域占据。废物以某种速度从一个地区转移到下一个地区。由于这个转移率可能是未知的，社会规划者可能对每个地区的责任有不确定性。在这种情况下分配成本的两种自然候选方法是将其预期责任分配给每个区域的方法，以及将其中值责任分配给每个区域的方法。我们证明后者等效于上游责任方法（Alcalde-Unzu et al. in Games Econ Behav 90:134–150, 2015），而前者是一种我们称之为预期责任的新方法。