The following is a presentation by Dr. Shalom Kelman of Baltimore, MD. Included is a brief description of the subject matter. For any questions and/or relevant material, please email shalomkelman@gmail.com
This Friday, Daf Yomi will be learning Kesubos Daf 93, the source of one of the most enigmatic sugyos in Shas. It deals with what Nobel Laureate Professor Robert Aumann has coined as the Talmud Bankruptcy Problem.
Three wives claim their Kesubos (valued at 100, 200, and 300, respectively) from their shared deceased husband's estate, valued at 100, 200, or 300. How does one achieve a fair division of the estate? The Mishna of R. Nosson proposes a solution that has baffled the sages for generations. The Gemara records that R. Yehuda HaNassi rejected R. Nosson's division.
Professor Aumann, using an arcane branch of mathematics known as Game Theory, successfully solved the enigma 30 years ago in a landmark paper (Game Theoretic Analysis of a Bankruptcy Problem from the Talmud Robert J. Aumann and Michael Maschler Journal of Economic Theory 36. 195-213 (1985)). Subsequently, he demonstrated that the principle of Shenayaim Ochzim B'Talis underlies this inexplicable division.
However, the line of reasoning followed by Aumann is challenging to follow except by a sophisticated mathematician. Dr. Fred Gross (in an unpublished manuscript) arrived at the same solution as Aumann, which is a closer approximation to the line of reasoning used by R. Nosson. Gross's proof utilizes introductory algebra that can be explained clearly to a lay audience.
Though Aumann and Gross pursue different approaches, their final equations and results remain equivalent.
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