Wednesday, July 20, 2011

Robert Aumann on the Talmud and Game Theory

NOBEL LAUREATE ROBERT AUMANN is interviewed on Arutz Sheva Radio about, inter alia, the Talmud and game theory. The key passage is here:
Douglas Goldstein: You used Game Theory to solve certain Talmudic problems in the Gemara and the Talmud. How does that work?

Robert Aumann: I will tell you the story. There is a passage in the Talmud in Ketubot 93a, and it has generated a tremendous amount of ink over thousands of years, and really there was great difficulty in understanding it. My son was killed in Lebanon in 1982.

I wrote him a letter once about a certain Talmudic issue and he wrote back Ketubot 93a and to look over there. I looked at this passage in the Talmud and I couldn’t figure it out. I, together with a colleague of mine, we looked at the numbers over there and they looked really, really odd. Then we decided to apply some game theoretic tools to try to understand this.

Eventually we found one of those tools which really fit the number perfectly, but this didn’t satisfy us yet because it’s a sophisticated modern mathematical concept and it’s unlikely the sages of the Talmud knew about this.

So we had to get to the bottom of the logic and this took us a few more months and finally we did arrive at it.

The sages of the Talmud were very smart and sophisticated. Obviously, they didn’t know modern mathematics but they did know logic. It’s quite possible that the logic that we found behind these numbers really was in the minds of the Talmudic sages.

It was also published in the Journal of Economic Theory in 1985 under the title “Game Theoretic Analysis of a Bankruptcy Problem from the Talmud.”

It’s hard to believe, but they worked out a Game Theoretic approach. They did reach the conclusions, which were not at all obvious, so I take off my hat to them.
More on Prof. Aumann's work on game theory and the Talmud is here.

On a tangentially related note, Mario I. Blejer has a piece on The Talmud and Greek Debt in Project Syndicate.