A bankruptcy problem occurs when several agents each claim a portion of an estate that is insufficient to satisfy all the claims, raising the question of how to divide the estate equitably among the agents.
In the traditional bankruptcy problem, there is a single decision made at a single point in time. Looking at the applications of bankruptcy, e.g. water sharing or vaccine allocation, one can see that these are actually problems where allocations have to be made over time. In this presentation, we introduce the concept of bankruptcy over time in the Multi-period Bankruptcy Problem. We also present three different perspectives on bankruptcy over time.
For each of these perspectives, we present mechanisms to generalize existing bankruptcy rules to the multi-period setting. Moreover, we formulate properties of these multi-period bankruptcy rules, and prove that these properties are inherited from the traditional bankruptcy rules. Finally, we present efficient algorithms to apply the bankruptcy rules using recursive methods.
By introducing the Multi-period Bankruptcy Problem, presenting and computing multi-period bankruptcy rules, we want to extend the usefulness of bankruptcy rules in practice and open avenues for further research on multi-period bankruptcy problems.