Equivalence of axioms for bankruptcy problems

The bankruptcy problem is concerned with how to divide the net worth of the bankrupt firm among its creditors. In this paper, we investigate the logical relations between various axioms in the context of bankruptcy. Those axioms are: population-and-resource monotonicity, consistency, converse consistency, agreement, and separability. In most axiomatic models, they are not directly related. However, we show that they are equivalent on the class of bankruptcy problems under minor additional requirements.