Thursday, July 28, 2005

Today's lecture

I just finished a attending a lecture by an Israeli game theorist.

His talk was rather interesting, though the second half was quite technical. He gave a talk generalizing the solution of Rabbi Natan in the Mishna (Ketubot 93b) regarding the division of an estate in cases where there were multiple claimants and not enough assets. The mishna gives a rather odd solution, and he showed that the solution was completely consistant with (Rashi's interpretation of) the garment solution (where two people claim different percentages of a garment). Generalizing this gets technical and involves the concept of the nucleolous the kernel and Shapley values and other complicated things, but it does generate a unique solution for all bankrupcy cases. Clearly Rabbi Nathan could not have had the generalized solution worked out but the intuition is pretty clever. It is clear now that he had in mind the concept of consistency with the rest of the mishna. Rabbi Nathan's student's had no idea why he proposed it. We do now. Moreover, using this it is possible to have a solution to bankrupcy cases we could not have had until the generalization was worked out. We also now know that there are unique solutions to all of this. There was aslo an interesting physical analogue of the proof.

At lunch he was quite amusing too. We spent an hour telling each other jokes.

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