Remarks on a surplus-sharing rule from the Mishneh Torah

Rabbi Moshe ben Maimon (1135-1204), known as Moses Maimonides, ranks among the most distinguished philosophers of the Middle Ages. He is the renowned author of the Mishneh Torah, a comprehensive code of Jewish law. Book 12 (‘Book of Acquisition’), Treatise 4 (‘Agents and Partners’), of the Code of Maimonides is devoted in Chapter 4 to the allocation of the surplus from funds which a partnership invests in an indivisible input. The Rabbi's case translates into a cooperative game where all intermediate coalitions are inessential. Standard axioms for cooperative-game solutions then suggest that the surplus be shared equally by the players, which is precisely the Maimonidean ruling. We show that this outcome can be preserved in spirit under much weaker assumptions on the worth of a game's intermediate coalitions. We present results both for the nucleolus and the Shapley value of the underlying class of games.