Bankruptcy problem

In mathematical sociology, and especially game theory, the bankruptcy problem is a distribution or entitlement problem involving the allocation of a given amount of a perfectly divisible good among a group of agents. The focus is on the case where the amount is insufficient to satisfy all their demands.

Problems of the bankruptcy type arise in many real life situations. The canonical example would be that of a bankrupt firm that is to be liquidated. Another example would be the division of an estate amongst several heirs, particularly when the estate cannot meet all the deceased’s commitments.

There are at least three simple methods for solving bankruptcy problems in practice, but each is deficient in one or more ways. The methods are:

1. The proportional rule: divide the estate proportionally to each agent's claim.
2. The constrained equal-awards rule: divide the estate equally among the agents, ensuring that nobody gets more than their claim.
3. The constrained equal-losses rule: divide equally the difference between the aggregate claim and the estate, ensuring that no agent ends up with a negative transfer.