INTERVIEW WITH ROBERT AUMANN
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good exercise: explain what you are doing to a smart person who has a general
understanding of the subject, but who is not from your discipline. It is one of the
great advantages of our Rationality Center. A lot of work here has been generated
from such discussions. Suddenly you realize that some of the basic premises of
your work may in fact be incorrect, or may need to be justified. The same goes
for collaborators. When you think by yourself, you gloss over things very quickly.
When you have to start explaining it to somebody, then you have to go very slowly,
step by step, and you cannot err so easily.
A: That’s entirely correct, and I’d like to back it up with a story from the Talmud.
A considerable part of the Talmud deals with pairs of sages, who consistently
argued with each other; one took one side of a question and the other took the
other side. One such pair was Rabbi Yochanan and Resh Lakish. They were
good friends, but also constantly taking opposite sides of any given question.
Then Resh Lakish died, and Rabbi Yochanan was inconsolable, grieved for many
days. Finally he returned to the study hall and resumed his lectures. Then, for
everything that Rabbi Yochanan said, one of the sages adduced thirty pieces of
supporting evidence. Rabbi Yochanan broke down in tears and said, what good are
you to me? You try to console me for the loss of Resh Lakish, but you do exactly
the opposite. Resh Lakish would come up with thirty challenges to everything
I said, thirty putative proofs that I am wrong. Then I would have to sharpen
my wits and try to prove that he is wrong and thereby my position would be
firmly established. Whereas you prove that I’m right. I know that I’m right; what
good does it do that you prove that I am right. It doesn’t advance knowledge at
all.
This is exactly your point. When you have different points of view and there is a
need to sharpen and solidify one’s own view of things, then arguing with someone
makes it much more acceptable, much better proved.
With many of my coauthors there were sharp disagreements and very close
bargaining as to how to phrase this or that. I remember an argument with Lloyd
Shapley at Stanford University one summer in the early seventies. I had broken
my foot in a rock-climbing accident. Shapley came to visit me in my room
at the Stanford Faculty Club, and I was hobbling around on crutches. This is
unbelievable, but we argued for a full half hour about a comma. I don’t remember
whether I wanted it in and Lloyd wanted it out, or the other way around. Neither
do I remember how it was resolved. It would not have been feasible to say “some
experts would put a comma here, others would not.” I always think that my
coauthors are stubborn, but maybe I am the stubborn one.
I will say one thing about coauthorship. Mike Maschler is a wonderful person
and a great scientist, but he is about the most stubborn person I know. One joint
paper with Maschler is about the bargaining set for cooperative games [17]. The
way this was born is that in my early days at the Hebrew University, in 1960,
I gave a math colloquium at which I presented the von Neumann–Morgenstern
stable set. In the question period, Mike said, I don’t understand this concept, it
sounds wrongheaded. I said, okay, let’s discuss it after the lecture. And we did.
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SERGIU HART
I tried to explain and to justify the stable set idea, which is beautiful and deep.
But Mike wouldn’t buy it. Exasperated, I finally said, well, can you do better?
He said, give me a day or two. A day or two passes and he comes back with
an idea. I shoot this idea down—show him why it’s no good. This continues
for about a year. He comes up with ideas for alternatives to stable sets, and I
shoot them down; we had well-defined roles in the process. Finally, he came up
with something that I was not able to shoot down with ease. We parted for the
summer. During that summer he wrote up his idea and sent it to me with a byline
of Robert Aumann and Michael Maschler. I said, I will have no part of this. I
can’t shoot it down immediately, but I don’t like the idea. Maschler wouldn’t take
no for an answer. He kept at me stubbornly for weeks and months and finally
I broke down and said, okay, I don’t like it, but go ahead and publish it. This
is the original “Bargaining Set for Cooperative Games” [17]. I still don’t like
that idea, but Maschler and Davis revised it and it eventually became, with their
revision, a very important concept, out of which grew the Davis–Maschler kernel
and Schmeidler’s nucleolus. Because of where it led more than because of what
it is, this became one of my most cited papers. Maschler’s stubbornness proved
justified. Maybe it should have waited for the Davis–Maschler revision in the first
place, but anyway, in hindsight I’m not sorry that we published this. Michael has
always been extremely stubborn. When he wants something, it gets done. As you
say, Sergiu, coauthorship is much more exacting, much more painful than writing
a paper alone, but it also leads to a better product.
H: This very naturally leads us to what you view as your main contributions.
And, what are your most cited papers, which may not be the same thing.
A: One’s papers are almost like one’s children and students—each one is dif-
ferent, one loves them all, and one does not compare them. Still, one does keep
abreast of what they’re doing; so I also keep an eye on the citations, which give a
sense of what the papers are “doing.”
One of the two most cited papers is the Equivalence Theorem—the “Markets
with a Continuum of Traders” [16]—the principle that the core is the same as
the competitive equilibrium in a market in which each individual player is negli-
gible. The other one is “Agreeing to Disagree” [34], which initiated “interactive
epistemology”—the formal theory of knowledge about others’ knowledge. After
that come the book with Shapley, Values of Non-Atomic Games [i], the two papers
on correlated equilibrium [29, 53], the bargaining set paper with Maschler [17],
the subjective probability paper with Anscombe [14], and “Integrals of Set-Valued
Functions” [21], a strictly mathematical paper that impacted control theory and
related areas as well as mathematical economics. The next batch includes the
repeated games work—the ’59 paper [4], the book with Maschler [v], the survey
[42], and the paper with Sorin on “Cooperation and Bounded Recall” [57]; also,
the Talmud paper with Maschler [46], the paper with Dr`eze on coalition structures
[31], the work with Brandenburger on “Epistemic Conditions for Nash Equilib-
rium” [65], the “Power and Taxes” paper with Kurz [37], some of the papers on
NTU-games [10, 24], and others.