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SERGIU HART
revision necessarily leads to the same probabilities. This question was raised—
and left open—in [29, Section 9j]. Indeed, even the formulation of the question
was murky.
I discussed this with Arrow and Frank Hahn during an IMSSS summer in the
early seventies. I remember the moment vividly. We were sitting in Frank Hahn’s
small office on the fourth floor of Stanford’s Encina Hall, where the economics
department was located. I was trying to get my head around the problem—not
its solution, but simply its formulation. Discussing it with them—describing the
issue to them—somehow sharpened and clarified it. I went back to my office, sat
down, and continued thinking. Suddenly the whole thing came to me in a flash—
the definition of common knowledge, the characterization in terms of information
partitions, and the agreement theorem: roughly, that if the probabilities of two
people for an event are commonly known by both, then they must be equal. It
took a couple of days more to get a coherent proof and to write it down. The
proof seemed quite straightforward. The whole thing—definition, formulation,
proof—came to less than a page.
Indeed, it looked so straightforward that it seemed hardly worth publishing. I
went back and told Arrow and Hahn about it. At first Arrow wouldn’t believe it,
but became convinced when he saw the proof. I expressed to him my doubts about
publication. He strongly urged me to publish it—so I did [34]. It became one of
my two most widely cited papers.
Six or seven years later I learned that the philosopher David Lewis had defined
the concept of common knowledge already in 1969, and, surprisingly, had used
the same name for it. Of course, there is no question that Lewis has priority. He
did not, however, have the agreement theorem.
H: The agreement theorem is surprising—and important. But your simple and
elegant formalization of common knowledge is even more important. It pioneered
the area known as “interactive epistemology”: knowledge about others’ knowl-
edge. It generated a huge literature—in game theory, economics, and beyond:
computer science, philosophy, logic. It enabled the rigorous analysis of very deep
and complex issues, such as what is rationality, and what is needed for equilibrium.
Interestingly, it led you in particular back to correlated equilibrium.
A: Yes. That’s paper [53]. The idea of common knowledge really enables the
“right” formulation of correlated equilibrium. It’s not some kind of esoteric exten-
sion of Nash equilibrium. Rather, it says that if people simply respond optimally
to their information—and this is commonly known—then you get correlated equi-
librium. The “equilibrium” part of this is not the point. Correlated equilibrium is
nothing more than just common knowledge of rationality, together with common
priors.
H: Let’s talk now about the Hebrew University. You came to the Hebrew
University in ’56 and have been there ever since.
A: I’ll tell you something. Mathematical game theory is a branch of applied
mathematics. When I was a student, applied mathematics was looked down
INTERVIEW WITH ROBERT AUMANN
699
upon by many pure mathematicians. They stuck up their noses and looked down
upon it.
H: At that time most applications were to physics.
A: Even that—hydrodynamics and that kind of thing—was looked down upon.
That is not the case anymore, and hasn’t been for quite a while; but in the late fifties
when I came to the Hebrew University that was still the vogue in the world of
mathematics. At the Hebrew University I did not experience any kind of inferiority
in that respect, nor in other respects either. Game theory was accepted as something
worthwhile and important. In fact, Aryeh Dvoretzky, who was instrumental in
bringing me here, and Abraham Fr¨ankel (of Zermelo–Fr¨ankel set theory), who
was chair of the mathematics department, certainly appreciated this subject. It was
one of the reasons I was brought here. Dvoretzky himself had done some work in
game theory.
H: Let’s make a big jump. In 1991, the Center for Rationality was established
at the Hebrew University.
A: I don’t know whether it was the brainchild of Yoram Ben-Porath or Menahem
Yaari or both together. Anyway, Ben-Porath, who was the rector of the university,
asked Yaari, Itamar Pitowsky, Motty Perry, and me to make a proposal for estab-
lishing a center for rationality. It wasn’t even clear what the center was to be called.
Something having to do with game theory, with economics, with philosophy. We
met many times. Eventually what came out was the Center for Rationality, which
you, Sergiu, directed for its first eight critical years; it was you who really got it
going and gave it its oomph. The Center is really unique in the whole world in that
it brings together very many disciplines. Throughout the world there are several
research centers in areas connected with game theory. Usually they are associated
with departments of economics: the Cowles Foundation at Yale, the Center for
Operations Research and Econometrics in Louvain, Belgium, the late Institute for
Mathematical Studies in the Social Sciences at Stanford. The Center for Rationality
at the Hebrew University is quite different, in that it is much broader. The basic
idea is “rationality”: behavior that advances one’s own interests. This appears in
many different contexts, represented by many academic disciplines. The Center
has members from mathematics, economics, computer science, evolutionary bi-
ology, general philosophy, philosophy of science, psychology, law, statistics, the
business school, and education. We should have a member from political science,
but we don’t; that’s a hole in the program. We should have one from medicine
too, because medicine is a field in which rational utility-maximizing behavior is
very important, and not at all easy. But at this time we don’t have one. There is
nothing in the world even approaching the breadth of coverage of the Center for
Rationality.
It is broad but nevertheless focused. There would seem to be a contradiction
between breadth and focus, but our Center has both—breadth and focus. The
breadth is in the number and range of different disciplines that are represented
at the Center. The focus is, in all these disciplines, on rational, self-interested
behavior—or the lack of it. We take all these different disciplines, and we look at