An ancient rabbinic rule for splitting debts hid a 1,800-year head start on game theory

A man dies owing 100, 200 and 300 coins to three creditors, but his estate holds only 100 coins. Ancient rabbinic law splits it equally: 33⅓ each. Raise the estate to 300 coins, and the very same law splits it 50 / 100 / 150. Raise it to 200, and it's 50 / 75 / 75. What single consistent rule produces all three splits?

Reveal the answer

In 1985, game theorists Robert Aumann and Michel Maschler showed these Mishnah-era numbers exactly match the 'nucleolus' — a cooperative game theory solution that treats each pairwise claim fairly and wasn't formally defined until 1969. The Talmud's ancient reasoners had landed on a mathematically consistent answer roughly 1,800 years early.

— Robert J. Aumann and Michel Maschler, Game Theoretic Analysis of a Bankruptcy Problem from the Talmud — Journal of Economic Theory, 1985

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