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I read an article a while back (maybe over a year ago?) in the Mishpacha English Magazine (I'm pretty sure, although it may have been in the Ami) that discussed a certain machlokes Tanaim about how to divide some disputed amount of money among different parties (that is all I remember of the case). There was a discussion if two people claim it, or three or more. Perhaps it was a discussion if someone stole something but doesn't know from who and there are several claimants it was them (but I'm not sure of that).

One of the opinions is very difficult to understand the theoretical basis behind, and the article quoted a Rishon as saying it is incomprehensible. The Halacha, of course, is paskened according to other opinions on how to do the division.

Then the article went on to say that that according to modern game theory this incomprehensible opinion was in fact comprehensible and consistent with this theory. I distinctly remember the specifics of the game theory not being discussed.

So which Machlokes Tanaim is this? What is the case, and the source? (The statement that one of the opinions is incomprehensible is probably enough to recognize it, but I have a feeling I'll recognize the case if I see it again).

Bonus points: What idea in Game theory helps explain the hard-to-understand opinion?

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    Are you referring to Dr. Aumann's discussion of the mishna in K'suvos (93a)?
    – Fred
    May 6, 2015 at 22:16
  • @Fred, I would think so yes. Thanks! Why not make it an answer?
    – Yishai
    May 6, 2015 at 22:34
  • @Fred, that particular paper has Dr Aumann's other explanations of the Mishna, not the Game Theory discussion that led to these other explanations.
    – J. C. Salomon
    May 7, 2015 at 1:04
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    @J.C.Salomon You're right, though that paper does mention the relevance of the "contested garment" condition (derived from the first mishna in Sh'nayim Ochazin). This is the original paper that discusses a generalized allocation model for the mishna, as well as a generalized game theoretic model to account for Sh'muel's explanation of the mishna.
    – Fred
    May 7, 2015 at 2:31
  • FWIW I heard from a pretty reliable source that last month someone challenged Dr. Aumann about a detail of his explanation of that Sugya at a presentation of his and he conceded the point for the time being. I don't know if any published adjustments/retractions are forthcoming or if the point was even very significant at all.
    – Double AA ♦
    May 7, 2015 at 3:38

1 Answer 1

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The discussion is indeed Dr. Aumann's discussion on Kesuvos 93a regarding the man who dies with insufficient funds to pay for his three wives' Kesubos. He claims to be the first to come up with this theory, but I think Rashi figured it out first. He theorizes as follows: First, award equally amongst all parties until one receives half of his claim. Then award equally among all other parties. Repeat until only one is left. Then continue awarding money to him until the difference between his claim and the amount he's getting equals the difference between his claim and the next guy's claim. Then award to the top two claimants equally. Repeat until all parties are receiving money again. Continue awarding money equally until everyone receives their claim.

As for the math behind it. I went over to the Math.SE to see what I could find out about this part. A fellow named Holger I Meinhardt answered the call here. (I tried copying it over, but apparently Mi Yodeya doesn't support MathJax.)

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