An explicit solution to a game-theoretic bankruptcy problem

This paper complements the breakthrough study by Aumann and Maschler on resolution of the conundrum from the Tractate of Kethuboth. The conundrum deals with the bankruptcy problem of the resources' allocation to the creditors when claims exceed the estate. The Mishnah and Talmud deal with three cases. Two of which did not raise questions, but the third case has perplexed Talmudic commentators over centuries. Aumann and Maschler provided the game theoretic framework for resolution of the asset distribution along with providing a rule, which leads to the numbers listed in the Mishnah. The paper series of Aumann and Maschler show the validity of Rabbi Nathan's argument who provided the ruling about the distribution. This study summarizes findings of previous studies on this subject and based on Kaminski's hydraulic rationing methodology - presents a closed-form solution for the resolution of the Talmudic conundrum, which also applies to an arbitrary number of creditors.