Another example of an important insight yielded by coalitional game

theory is the theory of matching markets. This whole branch of game

theory”and it is highly applied”grew out of the ™62 paper of Gale and

Shapley, “College Admissions and the Stability of Marriage.” It is not

quite as fundamental as the equivalence theorem, but it is a very import-

ant application, certainly of comparable importance to the work on

auctions in strategic game theory, which is very important. There is no

reason to denigrate the contributions of coalitional game theory, either

on the applied or the theoretical level.

Hart: Indeed, Adam Brandenburger said that his students at Harvard

Business School found cooperative game theory much more relevant to

them than the noncooperative theory.

Let™s switch to another topic. You have had an enormous impact on

the profession by in¬‚uencing many people. I am talking ¬rst of all about

your students. By now you have had 13 doctoral students. I think 12 of

them are by now professors, in Israel and abroad, who are well recog-

nized in the ¬eld and also in related ¬elds.

Aumann: Almost all the students eventually ended up in Israel, after a

short break for a postdoc or something similar abroad.

Hart: That™s not surprising since most of them”all except Wesley”

started in Israel and are Israelis.

Aumann: There is quite a brain drain from Israel. A large proportion

of prominent Israeli scientists who are educated in Israel end up abroad”

a much larger proportion than among my students.

These are my doctoral students up until now: Bezalel Peleg, David

Schmeidler, Shmuel Zamir, Binyamin Shitovitz, Zvi Artstein, Elon

Kohlberg, Sergiu Hart, Eugene Wesley, Abraham Neyman, Yair Tauman,

370 Sergiu Hart

Dov Samet, Ehud Lehrer, and Yossi Feinberg. Of these, three are cur-

rently abroad”Kohlberg, Wesley, and Feinberg. Also, there are about 30

or 40 masters students.

Each student is different. They are all great. In all cases I refused to

do what some people do, and that is to write a doctoral thesis for the

student. The student had to go and work it out by himself. In some

cases I gave very dif¬cult problems. Sometimes I had to backtrack and

suggest different problems, because the student wasn™t making progress.

There were one or two cases where a student didn™t make it”started

working and didn™t make progress for a year or two and I saw that he

wasn™t going to be able to make it with me. I informed him and he left.

I always had a policy of taking only those students who seemed very, very

good. I don™t mean good morally, but capable as scientists and spe-

ci¬cally as mathematicians. All of my students came from mathematics.

In most cases I knew them from my classes. In some cases not, and then

I looked carefully at their grades and accepted only the very best.

I usually worked quite closely with them, meeting once a week or so

at least, hearing about progress, making suggestions, asking questions.

When the ¬nal thesis was written I very often didn™t read it carefully.

Maybe this is news to Professor Hart, maybe it isn™t. But by that time I

knew the contents of the work because of the periodic meetings that we

would have.

Hart: Besides, you don™t believe anything unless you can prove it to

yourself.

Aumann: I read very little mathematics”only when I need to know.

Then, when reading an article I say, “Well, how does one prove this?”

Usually I don™t succeed, and then I look at the proof.

But it is really more interesting to hear from the students, so, Professor

Hart, what do you think?

Hart: Most doctoral students want to ¬nish their thesis and get out as

soon as possible. Aumann™s students usually want to continue”up to a

point, of course. This was one of the best periods in my life”being

immersed in research and bouncing ideas back and forth with Professor

Aumann; it was a very exciting period. It was very educating for my

whole life. Having a good doctoral adviser is a great investment for life.

There is a lot to say here, but it™s your interview, so I am making it very

short. There are many stories among your students, who are still very

close to one another.

Next, how about your collaborators? Shapley, Maschler, Kurz, and

Drèze are probably your major collaborators. Looking at your publica-

tions I see many other coauthors”a total of 20”but usually they are

more focused on one speci¬c topic.

An Interview with Robert Aumann 371

Figure 15.7 At the GAMES 1995 Conference in honor of Aumann™s

65th birthday, Jerusalem, June 1995. From left to right: Abraham Neyman,

Bob Aumann, John Nash, Reinhard Selten, Ken Arrow, and Sergiu Hart.

Aumann: I certainly owe a lot to all those people. Collaborating with

other people is a lot of work. It makes things a lot more dif¬cult, because

each person has his own angle on things and there are often disagree-

ments on conceptual aspects. It™s not like pure mathematics, where there

is a theorem and a proof. There may be disagreements about which

theorem to include and which theorem not to include, but there is no

room for substantive disagreement in a pure mathematics paper. Papers

in game theory or in mathematical economics have large conceptual com-

ponents, on which there often is quite substantial disagreement between

the coauthors, which must be hammered out. I experienced this with all

my coauthors.

You and I have written several joint papers, Sergiu. There wasn™t too

much disagreement about conceptual aspects there.

Hart: The ¬rst of our joint papers [Aumann and Hart (1986)] was

mostly mathematical, but over the last one [Aumann and Hart (2003)]

there was some . . . perhaps not disagreement, but clari¬cation of the con-

cepts. The other two papers, together with Motty Perry [Aumann, Hart,

and Perry (1997a,b)], involved a lot of discussion. I can also speak from

experience, having collaborated with other people, including some long-

standing collaborations. Beyond mathematics, the arguments are about

identifying the right concept. This is a question of judgment; one cannot

prove that this is a good concept and that is not. One can only have a

feeling or an intuition that that may lead to something interesting, that

372 Sergiu Hart

studying this may be interesting. Everybody brings his own intuitions

and ideas.

Aumann: But there are also sometimes real substantive disagreements.

There was a paper with Maschler”“Some Thoughts on the Minimax

Principle” [Aumann and Maschler (1972)]”where we had diametrically

opposed opinions on an important point that could not be glossed over.

In the end we wrote, “Some experts think A, others think ˜Not A.™ ”

That™s how we dealt with the disagreement. Often it doesn™t come to

that extreme, but there are substantial substantive disagreements with

coauthors. Of course these do not affect the major message of the paper.

But in the discussion, in the conceptualization, there are nuances over

which there are disagreements. All these discussions make writing a joint

paper a much more onerous affair than writing a paper alone. It becomes

much more time-consuming.

Hart: But it is time well consumed; having to battle for your opinion

and having to ¬nd better and better arguments to convince your coau-

thor is also good for your reader and is also good for really understand-

ing and getting much deeper into issues.

That is one reason why an interdisciplinary center is so good. When

you must explain your work to people who are outside your discipline,

you cannot take anything for granted. All the things that are somehow

commonly known and commonly accepted in your discipline suddenly

become questionable. Then you realize that in fact they shouldn™t be

commonly accepted. That is a very 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 justi¬ed. 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.

Aumann: 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