[Avodah] Game Theory and Bankruptcy

[Micha Berger]

Nobel Laureate R/Dr Robert Aumann famously (in our circles) explained
the distribution of funds in the mishnah on Kesuvos 93a. In that
mishnah, a man left behind 3 wives -- but the case works for 3
debts in general. Whatever wife 1's kesuvah is worth in the mishnah
would be the same as if 1 of 3 creditors were owed the same amount.

It is the creditor version that is the topic of AhS CM 104:15. But
it only holds in cases where the assets aren't real estate, or if
the debts are loans without certified contracts, if all the debts'
contracts have the same date -- in other words, in cases where one
doesn't pay the oldest loan fast.

Creditor A is owed 100 zuz, creditor B is owed 200 zuz, and creditor C,
300. And the debtor has left than 600 zuz to divide.

The AhS notes that there is a minority opinion that would have them divide
as we today would probably consider more intuitive -- proportionally.
A gets 1/6 of the assets, B gets 1/3 (ie 2/6) and C gets 1/2 (=3/6).
And in his day this was a common practice. So, while one may say this
became minhag hamaqom and thus a tenai implicitly accepted when doing
business or lending money, the AhS recommends that if the creditors
assume this division, beis din seek pesharah and divide this way.

However, iqar hadin is as per the mishnah. Which the gemara tells us
is R' Nasan, and R' Yehudah haNasi disagrees. (Stam mishnah, and the
redactor of mishnayos doesn't mention his own opinion???)

The first 100z has three claims on it and is divided in thirds.
The second 100z has two claims on it, and is divided equally between B & C.
And whatever is left is given to C.

What this means is that whomever has the biggest loan is most likely
to absorb the loss.

RRA explains this case in two papers. The first, aimed more at
mathematicians, invokes the Game Theoretic concept of nucleolus.
(R.J. Aumann and M. Maschler, Game Theoretic Analysis of a Bankruptcy
Problem from the Talmud, Journal of Economic Theory 36, no. 2 (1985),
195-213.) In the second, written for people who learn gemara, he avoids
all the technical talk. ("On the Matter of the Man with Three Wives,"
Moriah 22 (1999), 98- 107.)

The second paper compares this mishnah to the gemara at the opening of BM,
and derives a general rule, RAR saying that no other division in Qiddushin
would follow the same principles as the 2 person division in BM.
Here is an explanatory blog post <http://bit.ly/2IEmi4H> on Talmudology
blog ("Judaism, Science and Medicine"), by R/Dr Jeremy Brown.

(The blog would particularly be interesting to someone learning daf
who is interested in science or math.)

The aforementioned AhS gives two sevaras for R' Nasan's position:

The first is that the first division is taken from the
beinonis (mid-quality property) of the debtor's or the estate's
holdings. Therefore, it has to be divided separately from the rest of B &
C's debt. Each has claim to the full 100z, so each gets equally.

The second division is taken from the beinonis of what the person owned
that the time he started owing B & C money, and if there is non left,
from the ziburis (lesser quality). Again, different material, so it
is divided without consideration to the remainder of the debt to C.
merchandise. Therefore, it is accounted for separately

The second explanation focuses on why this case is different than
shutefus, where the shutefim do divide proportionally to their
investments.

The debtor's assets are entirely meshubadim to A just as much as to B
or C. C can't get his 300z until A's 100z is accounted for, no less than
the other way around -- each has full power to halt distribution of any
of the man's assets. So the division is by shibud, which is equal.
But with shutefim, the profit is clearcut.

:-)BBii!
-Micha

-- 
Micha Berger             It's never too late
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Fax: (270) 514-1507                      - George Eliot