that Rabbi Yochanan said, one of the sages adduced 30 pieces of sup-

porting evidence. Rabbi Yochanan broke down in tears and said, “What

An Interview with Robert Aumann 373

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 30

challenges to everything I said, 30 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 ¬rmly 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 argu-

ment 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 remem-

ber 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 [Aumann and Maschler (1964)]. 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. I tried to explain and to justify the stable set

idea, which is beautiful and deep. But Mike wouldn™t buy it. Exasper-

ated, I ¬nally 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-de¬ned 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

374 Sergiu Hart

stubbornly for weeks and months and ¬nally 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” [Aumann and Maschler (1964)].

I still don™t like that idea, but Maschler and Davis revised it and it event-

ually 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 justi¬ed. Maybe it should

have waited for the Davis“Maschler revision in the ¬rst place, but any-

way, 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.

Hart: This very naturally leads us to what you view as your main con-

tributions. And, what are your most cited papers, which may not be the

same thing.

Aumann: One™s papers are almost like one™s children and students”

each one is different, 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” [Aumann (1964)]”the prin-

ciple that the core is the same as the competitive equilibrium in a market

in which each individual player is negligible. The other one is “Agreeing to

Disagree” [Aumann (1976)], which initiated “interactive epistemology””

the formal theory of knowledge about others™ knowledge. After that

come the book with Shapley, Values of Non-Atomic Games [Aumann and

Shapley (1974)], the two papers on correlated equilibrium [Aumann

(1974, 1987)], the bargaining set paper with Maschler [Aumann

and Maschler (1964)], the subjective probability paper with Anscombe

[Aumann and Anscombe (1963)], and “Integrals of Set-Valued Func-

tions” [Aumann (1965)], 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 [Aumann

(1959)], the book with Maschler [Aumann and Maschler (1995)], the

survey [Aumann (1981)], and the paper with Sorin on “Cooperation and

Bounded Recall” [Aumann and Sorin (1989)]; also, the Talmud paper

with Maschler [Aumann and Maschler (1985)], the paper with Drèze

on coalition structures [Aumann and Drèze (1975)], the work with

Brandenburger on “Epistemic Conditions for Nash Equilibrium” [Aumann

and Brandenburger (1995)], the “Power and Taxes” paper with Kurz

An Interview with Robert Aumann 375

[Aumann and Kurz (1977a)], some of the papers on NTU-games

[Aumann (1961, 1967)], and others.

That sort of sums it up. Correlated equilibrium had a big impact. The

work on repeated games, the equivalence principle, the continuum of

players, interactive epistemology”all had a big impact.

Citations do give a good general idea of impact. But one should also

look at the larger picture. Sometimes there is a body of work that all

in all has a big impact, more than the individual citations show. In

addition to the above-mentioned topics, there is incomplete information,

NTU-values and NTU-games in general”with their many applications”

perfect and imperfect competition, utilities and subjective probabilities,

the mathematics of set-valued functions and measurability, extensive games,

and others. Of course, these are not disjoint; there are many interconnec-

tions and areas of overlap.

There is a joint paper with Jacques Drèze [Aumann and Drèze (1986)]

on which we worked very, very hard, for very, very long. For seven years

we worked on it. It contains some of the deepest work I have ever done.

It is hardly cited. This is a paper I love. It is nice work, but it hasn™t had

much of an impact.

Hart: Sometimes working very hard has two bad side effects. One is

that you have solved the problem and there is nothing more to say. Two,

it is so hard that nobody can follow it; it™s too hard for people to get into.

We were talking about various stations in your life. Besides City

College, MIT, Princeton, and Hebrew University you have spent a sig-

ni¬cant amount of time over the years at other places: Yale, Stanford,

CORE, and lately Stony Brook.

Aumann: Perhaps the most signi¬cant of all those places is Stanford

and, speci¬cally, the IMSSS, the Institute for Mathematical Studies in

the Social Sciences”Economics. This was run by Mordecai Kurz for 20

magni¬cent years between 1971 and 1990. The main activity of the

IMSSS was the summer gatherings, which lasted for six to eight weeks.

They brought together the best minds in economic theory. A lot of

beautiful economic theory was created at the IMSSS. The meetings were

relaxed, originally only on Tuesdays and Thursdays, with the whole morn-

ing devoted to one speaker; one or two speakers in the afternoon, not

more. A little later, Wednesday mornings also became part of the of¬cial

program. All the rest of the time was devoted to informal interaction

between the participants. Kenneth Arrow was a ¬xture there. So was

Frank Hahn. Of course, Mordecai. I came every year during that period.

It was an amazing place. Mordecai ran a very tight ship. One year he

even posted guards at the doors of the seminar room to keep uninvited

376 Sergiu Hart

people out. But he himself realized that that was going a little far, so that

lasted only that one summer.

Another anecdote from that period is this: the year after Arrow got

the Nobel Prize, he was vacationing in Hawaii at the beginning of July,

and did not turn up for the ¬rst session of the summer. Mordecai tracked

him down, phoned him and said, “Kenneth, what do you think you are

doing? You are supposed to be here; get on the next plane and come

down, or there will be trouble.” The audacity of the request is suf¬-

ciently astounding, but even more so is that Arrow did it. He cancelled