An interview with

AN INTERVIEW WITH ROBERT AUMANN ^

Interviewed by Sergiu Hart ^

Who is Robert Aumann? Is he an economist or a mathematician? A rational scientist or a deeply religious man? A deep thinker or an easygoing person?

These seemingly disparate qualities can all be found in Aumann; all are essential facets of his personality. A pure mathematician who is a renowned economist, he has been a central figure in developing game theory and establishing its key role in modern economics. He has shaped the field through his fundamental and pioneering work, work that is conceptually profound, and much of it also mathematically deep. He has greatly influenced and inspired many people: his students, collaborators, colleagues, and anyone who has been excited by reading his papers or listening to his talks.

Aumann promotes a unified view of rational behavior, in many different disciplines: chiefly economics, but also political science, biology, computer science, and more. He has broken new ground in many areas, the most notable being perfect competition, repeated games, correlated equilibrium, interactive knowledge and rationality, and coalitions and cooperation.

But Aumann is not just a theoretical scholar, closed in his ivory tower. He is interested in real-life phenomena and issues, to which he applies insights from his research. He is a devoutly religious man; and he is one of the founding fathers—and a central and most active member—of the multidisciplinary Center for the Study of Rationality at the Hebrew University in Jerusalem.

Aumann enjoys skiing, mountain climbing, and cooking—no less than working out a complex economic question or proving a deep theorem. He is a family man, a very warm and gracious person—of an extremely subtle and sharp mind.

This interview catches a few glimpses of Robert Aumann’s fascinating world. It was held in Jerusalem on three consecutive days in September 2004. I hope the reader will learn from it and enjoy it as much as we two did.
SH, Jerusalem, January 2005

Sergiu HART: Good morning, Professor Aumann. Well, I am not going to call you Professor Aumann. But what should I call you—Yisrael, Bob, Johnny?

Robert AUMANN: You usually call me Yisrael, so why don’t you continue to call me Yisrael. But there really is a problem with my given names. I have at least three given names—Robert, John, and Yisrael. Robert and John are my given names from birth and Yisrael is the name that I got at the circumcision. Many people call me Bob, which is of course short for Robert. There was once a trivia quiz at a students’ party at the Hebrew University, and one of the questions was, which faculty member has four given names and uses them all? Another story connected to my names is that my wife went to get approval of having our children included in her passport. She gave me the forms to sign on two different occasions. On one I signed Yisrael and on one I signed Robert. The clerk, when she gave him the forms, refused to accept them, saying, “Who is this man? Are there different fathers over here? We can’t accept this.”

H: I remember a time, when you taught at Tel Aviv University, you were filling out a form when suddenly you stopped and phoned your wife. “Esther,” you asked, “what’s my name in Tel Aviv?”

* * *

Let’s start with your scientific biography, namely, what were the milestones on your scientific route?

A: I did an undergraduate degree at City College in New York in mathematics, then on to MIT, where I did a doctorate with George Whitehead in algebraic topology, then on to a post-doc at Princeton with an operations research group affiliated with the math department. There I got interested in game theory. From there I went to the Hebrew University in Jerusalem, where I’ve been ever since. That’s the broad outline.

Now to fill that in a little bit. My interest in mathematics actually started in high school—the Rabbi Jacob Joseph Yeshiva (Hebrew Day School) on the lower east side of New York City. There was a marvelous teacher of mathematics there, by the name of Joseph Gansler. The classes were very small; the high school had just started operating. He used to gather the students around his desk. What really turned me on was geometry, theorems and proofs. So all the credit belongs to Joey Gansler.

Then I went on to City College. Actually I did a bit of soul-searching when finishing high school, on whether to become a Talmudic scholar, or study secular subjects at a university. For a while I did both. I used to get up in the morning at 6:15, go to the university in uptown New York from Brooklyn—an hour and a quarter on the subway—then study calculus for an hour, then go back to the yeshiva on the lower east side for most of the morning, then go back up to City College at 139^th Street and study there until 10 p.m., then go home and do some homework or whatever, and then I would get up again at 6:15. I did this for one semester, and then it became too much for me and I made the hard decision to quit the yeshiva and study mathematics.


Picture 1. Bob Aumann, circa 2000
H: How did you make the decision?

A: I really can’t remember. I know the decision was mine. My parents put a lot of responsibility on us children. I was all of seventeen at the time, but there was no overt pressure from my parents. Probably math just attracted me more, although I was very attracted by Talmudic studies.

At City College, there was a very active group of mathematics students. The most prominent of the mathematicians on the staff was Emil Post, a famous logician. He was in the scientific school of Turing and Church—mathematical logic, computability—which was very much the “in” thing at the time. This was the late forties. Post was a very interesting character. I took just one course from him and that was functions of real variables—measure, integration, etc. The entire course consisted of his assigning exercises and then calling on the students to present the solutions on the blackboard. It’s called the Moore method—no lectures, only exercises. It was a very good course. There were also other excellent teachers there, and there was a very active group of mathematics students. A lot of socializing went on. There was a table in the cafeteria called the mathematics table. Between classes we would sit there and have ice cream and—

H: Discuss the topology of bagels?

A: Right, that kind of thing. A lot of chess playing, a lot of math talk. We ran our own seminars, had a math club. Some very prominent mathematicians came out of there—Jack Schwartz of Dunford–Schwartz fame, Leon Ehrenpreis, Alan Shields, Leo Flatto, Martin Davis, D. J. Newman. That was a very intense experience. From there I went on to graduate work at MIT, where I did a doctorate in algebraic topology with George Whitehead.

Let me tell you something very moving relating to my thesis. As an undergraduate, I read a lot of analytic and algebraic number theory. What is fascinating about number theory is that it uses very deep methods to attack problems that are in some sense very “natural” and also simple to formulate. A schoolchild can understand Fermat’s last theorem, but it took extremely deep methods to prove it. A schoolchild can understand what a prime number is, but understanding the distribution of prime numbers requires the theory of functions of a complex variable; it is closely related to the Riemann hypothesis, whose very formulation requires at least two or three years of university mathematics, and which remains unproved to this day. Another interesting aspect of number theory was that it was absolutely useless—pure mathematics at its purest.

In graduate school, I heard George Whitehead’s excellent lectures on algebraic topology. Whitehead did not talk much about knots, but I had heard about them, and they fascinated me. Knots are like number theory: the problems are very simple to formulate, a schoolchild can understand them; and they are very natural, they have a simplicity and immediacy that is even greater than that of prime numbers or Fermat’s last theorem. But it is very difficult to prove anything at all about them; it requires really deep methods of algebraic topology. And, like number theory, knot theory was totally, totally useless.

So, I was attracted to knots. I went to Whitehead and said, I want to do a PhD with you, please give me a problem. But not just any problem; please, give me an open problem in knot theory. And he did; he gave me a famous, very difficult problem—the “asphericity” of knots—that had been open for twenty-five years and had defied the most concerted attempts to solve.

Though I did not solve that problem, I did solve a special case. The complete statement of my result is not easy to formulate for a layman, but it does have an interesting implication that even a schoolchild can understand and that had not been known before my work: alternating knots do not “come apart,” cannot be separated.

So, I had accomplished my objective—done something that i) is the answer to a “natural” question, ii) is easy to formulate, iii) has a deep, difficult proof, and iv) is absolutely useless, the purest of pure mathematics.

It was in the fall of 1954 that I got the crucial idea that was the key to proving my result. The thesis was published in the Annals of Mathematics in 1956 [1]; but the proof was essentially in place in the fall of 1954. Shortly thereafter, my research interests turned from knot theory to the areas that have occupied me to this day.

That’s Act I of the story. And now, the curtain rises on Act II—fifty years later, almost to the day. It’s 10 p.m., and the phone rings in my home. My grandson Yakov Rosen is on the line. Yakov is in his second year of medical school. “Grandpa,” he says, “can I pick your brain? We are studying knots. I don’t understand the material, and think that our lecturer doesn’t understand it either. For example, could you explain to me what, exactly, are ‘linking numbers’?” “Why are you studying knots?” I ask; “what do knots have to do with medicine?” “Well,” says Yakov, “sometimes the DNA in a cell gets knotted up. Depending on the characteristics of the knot, this may lead to cancer. So, we have to understand knots.”

I was completely bowled over. Fifty years later, the “absolutely useless”—the “purest of the pure”—is taught in the second year of medical school, and my grandson is studying it. I invited Yakov to come over, and told him about knots, and linking numbers, and my thesis.

H: This is indeed fascinating. Incidentally, has the “big, famous” problem ever been solved?

A: Yes. About a year after my thesis was published, a mathematician by the name of Papakyriakopoulos solved the general problem of asphericity. He had been working on it for eighteen years. He was at Princeton, but didn’t have a job there; they gave him some kind of stipend. He sat in the library and worked away on this for eighteen years! During that whole time he published almost nothing—a few related papers, a year or two before solving the big problem. Then he solved this big problem, with an amazingly deep and beautiful proof. And then, he disappeared from sight, and was never heard from again. He did nothing else. It’s like these cactuses that flower once in eighteen years. Naturally that swamped my result; fortunately mine came before his. It swamped it, except for one thing. Papakyriakopoulos’s result does not imply that alternating knots will not come apart. What he proved is that a knot that does not come apart is aspheric. What I proved is that all alternating knots are aspheric. It’s easy to see that a knot that comes apart is not aspheric, so it follows that an alternating knot will not come apart. So that aspect of my thesis—which is the easily formulated part—did survive.

A little later, but independently, Dick Crowell also proved that alternating knots do not come apart, using a totally different method, not related to asphericity.

* * *

H: Okay, now that we are all tied up in knots, let’s untangle them and go on. You did your PhD at MIT in algebraic topology, and then what?

A: Then for my post-doc, I joined an operations research group at Princeton. This was a rather sharp turn because algebraic topology is just about the purest of pure mathematics and operations research is very applied. It was a small group of about ten people at the Forrestal Research Center, which is attached to Princeton University.

H: In those days operations research and game theory were quite connected. I guess that’s how you—

A: —became interested in game theory, exactly. There was a problem about defending a city from a squadron of aircraft most of which are decoys—do not carry any weapons—but a small percentage do carry nuclear weapons. The project was sponsored by Bell Labs, who were developing a defense missile.

At MIT I had met John Nash, who came there in ’53 after doing his doctorate at Princeton. I was a senior graduate student and he was a Moore instructor, which was a prestigious instructorship for young mathematicians. So he was a little older than me, scientifically and also chronologically. We got to know each other fairly well and I heard from him about game theory. One of the problems that we kicked around was that of dueling—silent duels, noisy duels, and so on. So when I came to Princeton, although I didn’t know much about game theory at all, I had heard about it; and when we were given this problem by Bell Labs, I was able to say, this sounds a little bit like what Nash was telling us; let’s examine it from that point of view. So I started studying game theory; the rest is history, as they say.

H: You started reading game theory at that point?

A: I just did the minimum necessary of reading in order to be able to attack the problem.

H: Who were the game theorists at Princeton at the time? Did you have any contact with them?

A: I had quite a bit of contact with the Princeton mathematics department. Mainly at that time I was interested in contact with the knot theorists, who included John Milnor and of course R. H. Fox, who was the high priest of knot theory. But there was also contact with the game theorists, who included Milnor—who was both a knot theorist and a game theorist—Phil Wolfe, and Harold Kuhn. Shapley was already at RAND; I did not connect with him until later.

In ’56 I came to the Hebrew University. Then, in ’60–’61, I was on sabbatical at Princeton, with Oskar Morgenstern’s outfit, the Econometric Research Program. This was associated with the economics department, but I also spent quite a bit of time in Fine Hall, in the mathematics department.

Let me tell you an interesting anecdote. When I felt it was time to go on sabbatical, I started looking for a job, and made various applications. One was to Princeton—to Morgenstern. One was to IBM Yorktown Heights, which was also quite a prestigious group. I think Ralph Gomory was already the director of the math department there. Anyway, I got offers from both. The offer from IBM was for $14,000 per year. $14,000 doesn’t sound like much, but in 1960 it was a nice bit of money; the equivalent today is about $100,000, which is a nice salary for a young guy just starting out. Morgenstern offered $7,000, exactly half. The offer from Morgenstern came to my office and the offer from IBM came home; my wife Esther didn’t open it. I naturally told her about it and she said, “I know why they sent it home. They wanted me to open it.”

I decided to go to Morgenstern. Esther asked me, “Are you sure you are not doing this just for ipcha mistabra?,” which is this Talmudic expression for doing just the opposite of what is expected. I said, “Well, maybe, but I do think it’s better to go to Princeton.” Of course I don’t regret it for a moment. It is at Princeton that I first saw the Milnor–Shapley paper, which led to the “Markets with a Continuum of Traders” [16], and really played a major role in my career; and I have no regrets over the career.

H: Or you could have been a main contributor to computer science.

A: Maybe, one can’t tell. No regrets. It was great, and meeting Morgenstern and working with him was a tremendous experience, a tremendous privilege.

H: Did you meet von Neumann?

A: I met him, but in a sense, he didn’t meet me. We were introduced at a game theory conference in 1955, two years before he died. I said, “Hello, Professor von Neumann,” and he was very cordial, but I don’t think he remembered me afterwards unless he was even more extraordinary than everybody says. I was a young person and he was a great star.

But Morgenstern I got to know very, very well. He was extraordinary. You know, sometimes people make disparaging remarks about Morgenstern, in particular about his contributions to game theory. One of these disparaging jokes is that Morgenstern’s greatest contribution to game theory is von Neumann. So let me say, maybe that’s true—but that is a tremendous contribution. Morgenstern’s ability to identify people, the potential in people, was enormous and magnificent, was wonderful. He identified the economic significance in the work of people like von Neumann and Abraham Wald, and succeeded in getting them actively involved. He identified the potential in many others; just in the year I was in his outfit, Clive Granger, Sidney Afriat, and Reinhard Selten were also there.

Picture 2. Sergiu Hart, Mike Maschler, Bob Aumann, Bob Wilson, and Oskar Morgenstern, at the 1994 Morgenstern Lecture, Jerusalem

Morgenstern had his own ideas and his own opinions and his own important research in game theory, part of which was the von Neumann–Morgenstern solution to cooperative games. And, he understood the importance of the minimax theorem to economics. One of his greatnesses was that even though he could disagree with people on a scientific issue, he didn’t let that interfere with promoting them and bringing them into the circle.

For example, he did not like the idea of perfect competition and he did not like the idea of the core; he thought that perfect competition is a mirage, that when there are many players, perfect competition need not result. And indeed, if you apply the von Neumann–Morgenstern solution, it does not lead to perfect competition in markets with many people—that was part of your doctoral thesis, Sergiu. So even though he thought that things like core equivalence were wrongheaded, he still was happy and eager to support people who worked in this direction.

At Princeton I also got to know Frank Anscombe—

H: —with whom you wrote a well-known and influential paper [14]—

A: —that was born then. At that time the accepted definition of subjective probability was Savage’s. Anscombe was giving a course on the foundations of probability; he gave a lot of prominence to Savage’s theory, which was quite new at the time. Savage’s book had been published in ’54; it was only six years old. As a result of this course, Anscombe and I worked out this alternative definition, which was published in 1963.

H: You also met Shapley at that time?

A: Well, being in game theory, one got to know the name; but personally I got to know Shapley only later. At the end of my year at Princeton, in the fall of ’61, there was a conference on “Recent Developments in Game Theory,” chaired by Morgenstern and Harold Kuhn. The outcome was the famous orange book, which is very difficult to obtain nowadays. I was the office boy, who did a lot of the practical work in preparing the conference. Shapley was an invited lecturer, so that is the first time I met him.

Another person about whom the readers of this interview may have heard, and who gave an invited lecture at that conference, was Henry Kissinger, who later became the Secretary of State of the United States and was quite prominent in the history of Israel. After the Yom Kippur War in 1973, he came to Israel and to Egypt to try to broker an arrangement between the two countries. He shuttled back and forth between Cairo and Jerusalem. When in Jerusalem, he stayed at the King David Hotel, which is acknowledged to be the best hotel here. Many people were appalled at what he was doing, and thought that he was exercising a lot of favoritism towards Egypt. One of these people was my cousin Steve Strauss, who was the masseur at the King David. Kissinger often went to get a massage from Steve. Steve told us that whenever Kissinger would, in the course of his shuttle diplomacy, do something particularly outrageous, he would slap him really hard on the massage table. I thought that Steve was kidding, but this episode appears also in Kissinger’s memoirs; so there is another connection between game theory and the Aumann family.

At the conference, Kissinger spoke about game-theoretic thinking in Cold War diplomacy, Cold War international relations. It is difficult to imagine now how serious the Cold War was. People were really afraid that the world was coming to an end, and indeed there were moments when it did seem that things were hanging in the balance. One of the most vivid was the Cuban Missile Crisis in 1963. In his handling of that crisis, Kennedy was influenced by the game-theoretic school in international relations, which was quite prominent at the time. Kissinger and Herman Kahn were the main figures in that. Kennedy is now praised for his handling of that crisis; indeed, the proof of the pudding is in the eating of it—it came out well. But at that time it seemed extremely hairy, and it really looked as if the world might come to an end at any moment—not only during the Cuban Missile Crisis, but also before and after.

The late fifties and early sixties were the acme of the Cold War. There was a time around ’60 or ’61 when there was this craze of building nuclear fallout shelters. The game theorists pointed out that this could be seen by the Russians as an extremely aggressive move. Now it takes a little bit of game-theoretic thinking to understand why building a shelter can be seen as aggressive. But the reasoning is quite simple. Why would you build shelters? Because you are afraid of a nuclear attack. Why are you afraid of a nuclear attack? Well, one good reason to be afraid is that if you are going to attack the other side, then you will be concerned about retaliation. If you do not build shelters, you leave yourself open. This is seen as conciliatory because then you say, I am not concerned about being attacked because I am not going to attack you. So building shelters was seen as very aggressive and it was something very real at the time.

H: In short, when you build shelters, your cost from a nuclear war goes down, so your incentive to start a war goes up.

* * *

Since you started talking about these topics, let’s perhaps move to Mathematica, the United States Arms Control and Disarmament Agency (ACDA), and repeated games. Tell us about your famous work on repeated games. But first, what are repeated games?

A: It’s when a single game is repeated many times. How exactly you model “many” may be important, but qualitatively speaking, it usually doesn’t matter too much.

H: Why are these models important?

A: They model ongoing interactions. In the real world we often respond to a given game situation not so much because of the outcome of that particular game as because our behavior in a particular situation may affect the outcome of future situations in which a similar game is played. For example, let’s say somebody promises something and we respond to that promise and then he doesn’t keep it—he double-crosses us. He may turn out a winner in the short term, but a loser in the long term: if I meet up with him again and we are again called upon to play a game—to be involved in an interactive situation—then the second time around I won’t trust him. Whether he is rational, whether we are both rational, is reflected not only in the outcome of the particular situation in which we are involved today, but also in how it affects future situations.

Another example is revenge, which in the short term may seem irrational; but in the long term, it may be rational, because if you take revenge, then the next time you meet that person, he will not kick you in the stomach. Altruistic behavior, revengeful behavior, any of those things, make sense when viewed from the perspective of a repeated game, but not from the perspective of a one-shot game. So, a repeated game is often more realistic than a one-shot game: it models ongoing relationships.

In 1959 I published a paper on repeated games [4]. The brunt of that paper is that cooperative behavior in the one-shot game corresponds to equilibrium or egotistic behavior in the repeated game. This is to put it very simplistically.