On solving mutual liability problems

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 [Formula: see text] -transfer schemes, which are based on a bankruptcy rule [Formula: see text] . Although in general a [Formula: see text] -transfer scheme need not be unique, we show that the resulting [Formula: see text] -transfer allocation is. This leads to the definition of [Formula: see text] -based mutual liability rules. For so called hierarchical mutual liability problems an alternative characterization of [Formula: see text] -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.