Multi-Period Bankruptcy Problems

Although temporal considerations are inherent to real-life allocation problems, extensions of bankruptcy problems to a multi-period setting remain largely underexplored. We introduce the concept of bankruptcy over time in the Multi-period Bankruptcy Problem and are the first to examine whether, and how, unmet demand from previous periods can be incorporated into such settings. Therefore, we present and analyze two complementary perspectives on multiperiod bankruptcy problems to generalize existing bankruptcy rules to the multi-period setting. Moreover, we formulate properties of these multi-period bankruptcy rules and prove that they are valid extensions of their single-period counterparts. Based on these properties, we derive characterizations of the multi-period extensions of two of the most widely used single-period bankruptcy rules: the constrained equal awards rule and the proportional rule. By introducing the Multi-period Bankruptcy Problem and presenting multi-period bankruptcy rules, we aim to extend the use of bankruptcy rules in practice and open avenues for further research on multi-period bankruptcy problems.