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Sequential sharing rules for river sharing problems

机译：河流共享问题的顺序共享规则

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摘要

We analyse the redistribution of a resource amongst agents who have claims to the resource and who are ordered linearly. A well known example of this particular situation is the river sharing problem. We exploit the linear order of agents to transform the river sharing problem to a sequence of two-agent river sharing problems. These reduced problems are mathematically equivalent to bankruptcy problems and can therefore be solved using any bankruptcy rule. Our proposed class of solutions, that we call sequential sharing rules, solves the river sharing problem. Our approach extends the bankruptcy literature to settings with a sequential structure of both the agents and the resource to be shared. In the paper, we first characterise the class of sequential sharing rules. Subsequently, we apply sequential sharing rules based on four classical bankruptcy rules, assess their properties, provide two characterisations of one specific rule, and compare sequential sharing rules with three alternative solutions to the river sharing problem.
机译：我们分析了在对资源有要求并线性排序的代理商之间资源的重新分配。这种特殊情况的一个众所周知的例子是河流共享问题。我们利用主体的线性顺序将河流共享问题转换为一系列两主体河流共享问题。从数学上讲，这些减少的问题等同于破产问题，因此可以使用任何破产规则来解决。我们提出的一类解决方案（称为顺序共享规则）解决了河流共享问题。我们的方法将破产文献扩展到具有代理和要共享资源的顺序结构的设置。在本文中，我们首先描述了顺序共享规则的类别。随后，我们基于四个经典破产规则应用顺序共享规则，评估它们的性质，提供一个特定规则的两个特征，然后将顺序共享规则与河流共享问题的三种替代解决方案进行比较。

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