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.

Hart: 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 ¬rst, what are repeated games?

Aumann: 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.

Hart: Why are these models important?

Aumann: 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

An Interview with Robert Aumann 337

both rational, is re¬‚ected 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 [Aumann (1959)]. 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.

Hart: There is the famous “Folk Theorem.” In the seventies you named

it, in your survey of repeated games [Aumann (1981)]. The name has

stuck. Incidentally, the term “folk theorem” is nowadays also used in

other areas for classic results: the folk theorem of evolution, of comput-

ing, and so on.

Aumann: The original Folk Theorem is quite similar to my ™59 paper,

but a good deal simpler, less deep. As you said, that became quite

prominent in the later literature. I called it the Folk Theorem because its

authorship is not clear, like folk music, folk songs. It was in the air in the

late ¬fties and early sixties.

Hart: Yours was the ¬rst full formal statement and proof of something

like this. Even Luce and Raiffa, in their very in¬‚uential ™57 book, Games

and Decisions, don™t have the Folk Theorem.

Aumann: The ¬rst people explicitly to consider repeated non-zero-

sum games of the kind treated in my ™59 paper were Luce and Raiffa. But

as you say, they didn™t have the Folk Theorem. Shubik™s book Strategy

and Market Structure, published in ™59, has a special case of the Folk

Theorem, with a proof that has the germ of the general proof.

At that time people did not necessarily publish everything they knew”

in fact, they published only a small proportion of what they knew, only

really deep results or something really interesting and nontrivial in the

mathematical sense of the word”which is not a good sense. Some of the

things that are most important are things that a mathematician would

consider trivial.

Hart: I remember once in class that you got stuck in the middle of a

proof. You went out, and then came back, thinking deeply. Then you

went out again. Finally you came back some 20 minutes later and said,

“Oh, it™s trivial.”

338 Sergiu Hart

Aumann: Yes, I got stuck and started thinking; the students were quiet

at ¬rst, but got noisier and noisier, and I couldn™t think. I went out and

paced the corridors and then hit on the answer. I came back and said,

“This is trivial”; the students burst into laughter. So “trivial” is a bad term.

Take something like the Cantor diagonal method. Nowadays it would

be considered trivial, and sometimes it really is trivial. But it is extremely

important; for example, Gödel™s famous incompleteness theorem is based

on it.

Hart: “Trivial to explain” and “trivial to obtain” are different. Some of

the confusion lies there. Something may be very simple to explain once

you get it. On the other hand, thinking about it and getting to it may be

very deep.

Aumann: Yes, and hitting on the right formulation may be very

important. The diagonal method illustrates that even within pure

mathematics the trivial may be important. But certainly outside of it,

there are interesting observations that are mathematically trivial”like the

Folk Theorem. I knew about the Folk Theorem in the late ¬fties, but

was too young to recognize its importance. I wanted something deeper,

and that is what I did in fact publish. That™s my ™59 paper [Aumann

(1959)]. It™s a nice paper”my ¬rst published paper in game theory

proper. But the Folk Theorem, although much easier, is more important.

So it™s important for a person to realize what™s important. At that time I

didn™t have the maturity for this.

Quite possibly, other people knew about it. People were thinking about

repeated games, dynamic games, long-term interaction. There are Shapley™s

stochastic games, Everett™s recursive games, the work of Gillette, and so

on. I wasn™t the only person thinking about repeated games. Anybody

who thinks a little about repeated games, especially if he is a mathemat-

ician, will very soon hit on the Folk Theorem. It is not deep.

Hart: That™s ™59; let™s move forward.

Aumann: In the early sixties Morgenstern and Kuhn founded a con-

sulting ¬rm called Mathematica, based in Princeton, not to be confused

with the software that goes by that name today. In ™64 they started

working with the United States Arms Control and Disarmament Agency.

Mike Maschler worked with them on the ¬rst project, which had to

do with inspection; obviously there is a game between an inspector and

an inspectee, who may want to hide what he is doing. Mike made an

important contribution to that. There were other people working on that

also, including Frank Anscombe. This started in ™64, and the second

project, which was larger, started in ™65. It had to do with the Geneva

disarmament negotiations, a series of negotiations with the Soviet Union,

on arms control and disarmament. The people on this project included

An Interview with Robert Aumann 339

Kuhn, G©rard Debreu, Herb Scarf, Reinhard Selten, John Harsanyi,

Jim Mayberry, Maschler, Dick Stearns (who came in a little later), and

me. What struck Maschler and me was that these negotiations were taking

place again and again; a good way of modeling this is a repeated game.

The only thing that distinguished it from the theory of the late ¬fties that

we discussed before is that these were repeated games of incomplete

information. We did not know how many weapons the Russians held,

and the Russians did not know how many weapons we held. What we”

the United States”proposed to put into the agreements might in¬‚uence

what the Russians thought or knew that we had, and this would affect

what they would do in later rounds.

Hart: What you do reveals something about your private information.

For example, taking an action that is optimal in the short run may reveal

to the other side exactly what your situation is, and then in the long run

you may be worse off.

Aumann: Right. This informational aspect is absent from the previous

work, where everything was open and above board, and the issues are

how one™s behavior affects future interaction. Here the question is how

one™s behavior affects the other player™s knowledge. So Maschler and I,

and later Stearns, developed a theory of repeated games of incomplete

information. This theory was set forth in a series of research reports

between ™66 and ™68, which for many years were unavailable.

Hart: Except to the a¬cionados, who were passing bootlegged copies

from mimeograph machines. They were extremely hard to ¬nd.

Aumann: Eventually they were published by MIT Press in ™95 [Aumann

and Maschler (1995)], together with extensive postscripts describing

what has happened since the late sixties”a tremendous amount of work.

The mathematically deepest started in the early seventies in Belgium, at

CORE, and in Israel, mostly by my students and then by their students.

Later it spread to France, Russia, and elsewhere. The area is still active.