690
SERGIU HART
F
IGURE
2. Sergiu Hart, Mike Maschler, Bob Aumann, Bob Wilson, and Oskar Morgenstern,
at the 1994 Morgenstern Lecture, Jerusalem.
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 per-
fect 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
INTERVIEW WITH ROBERT AUMANN
691
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.
692
SERGIU HART
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.
H: There is the famous “Folk Theorem.” In the seventies you named it, in your
survey of repeated games [42]. 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 computing, and so on.
A: 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 fifties and early sixties.
H: Yours was the first full formal statement and proof of something like this.
Even Luce and Raiffa, in their very influential ’57 book, Games and Decisions,
don’t have the Folk Theorem.
A: The first 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.
Dostları ilə paylaş: |