The bankruptcy problem is as old as money itself. The main challenge to analyzing ancient solutions to the bankruptcy problem is that these solutions are often presented not as a general algorithm, but rather as a series of examples. Whenever those example sare few in number, it is often difficult to derive the underlying algorithm. This was the case, for example, with the Talmudic solution to the bankruptcy problem. Only in themid-1980s did Nobelist Robert Aumann succeed in cracking the algorithm underlying the Talmudic “Bankruptcy Code”. Aumann used game theory techniques to crack the code but did not delve into the question of whether such code was fair. In this paper we attempt to answer that question.
Introduction
A person or company goes bankrupt when they can no longer satisfy their obligations in full. Available funds (the estate) are then distributed among the claimants. Since there is not enough money to satisfy everybody in full, at least some claimants will recover less than they’re owed. How much less? Is there a fair way to divide the estate among the claimants?
The Talmudic Solution to the Bankruptcy Problem The bankruptcy problem is as old as money itself and solutions to the problem have been proposed for about just as long. One ancient solution is posited in the Babylonian Talmud (Ketubot 93a, Bava Metzia 2a, and Yevamot 38a).
Like many ancient texts dealing with numbers, the Talmud does not offer an explicit algorithm. Instead, it puts forward four examples illustrating how an estate (E) should be divided. In the first three examples, three parties are owed the following amounts:
