This paper introduces mutual liability problems, as a generalization of bankruptcy problems, where every agent not only owns a certain amount of cash money, but also has outstanding claims and debts towards the other agents. Assuming that the agents want to cash their claims, we will analyze mutual liability rules which prescribe how the total available amount of cash should be allocated among the agents. We in particular focus on bilateral \(\varphi \)-transfer schemes, which are based on a bankruptcy rule \(\varphi \). Although in general a \(\varphi \)-transfer scheme need not be unique, we show that the resulting \(\varphi \)-transfer allocation is. This leads to the definition of \(\varphi \)-based mutual liability rules. For so called hierarchical mutual liability problems an alternative characterization of \(\varphi \)-based mutual liability rules is provided. Moreover it is shown that the axiomatic characterization of the Talmud rule on the basis of consistency can be extended to the corresponding mutual liability rule.

中文翻译：

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关于解决共同责任问题。

本文介绍了相互责任问题，作为破产问题的概括，其中每个代理人不仅拥有一定数量的现金，而且对其他代理人都有未偿还的债权和债务。假设代理商想兑现其索赔，我们将分析相互责任规则，该规则规定了应如何在代理商之间分配现金总量。我们特别关注基于破产规则\（\ varphi \）的双边\（\ varphi \）-转移方案。尽管通常\（\ varphi \）- transfer方案不一定是唯一的，但我们证明了生成的\（\ varphi \）- transfer分配是唯一的。这导致\（\ varphi \）的定义的共同责任规则。对于所谓的分层共同责任问题，提供了基于\（\ varphi \）的共同责任规则的替代特征。此外，表明基于一致性的塔尔木德规则的公理化特征可以扩展到相应的共同责任规则。