On Solving Liability Problems

This paper introduces 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 liability rules which prescribe how the total available amount of cash should be allocated among the agents. In particular we focus on bankruptcy rule based bilateral transfer schemes. Existence of these schemes is established and it is seen that within the class of hierarchical liability problems, such a transfer scheme is unique. Although in general a bankruptcy rule based bilateral transfer scheme need not be unique, we show that the resulting bankruptcy rule based transfer allocation is. This leads to the definition of bankruptcy rule based liability rules. For hierarchical liability problems an alternative characterization of such liability rules is provided. Moreover it is shown that the axiomatic characterization of the Aumann-Maschler bankruptcy rule on the basis of consistency can be extended to the corresponding liability rule. We conclude with a discussion of alternative approaches to solve liability problems