An interview with robert aumann
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INTERVIEW WITH ROBERT AUMANN 693 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. H: 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 twenty minutes later and said, “Oh, it’s trivial.”
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 con- sidered trivial, and sometimes it really is trivial. But it is extremely important; for example, G¨odel’s famous incompleteness theorem is based on it.
sion 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.
agonal 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 fifties, 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 [4]. It’s a nice paper—my first 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 mathematician, will very soon hit on the Folk Theorem. It is not deep.
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 first 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 Kuhn, Gerard Debreu, Herb Scarf, Reinhard
694 SERGIU HART 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 fifties 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 influence what the Russians thought or knew that we had, and this would affect what they would do in later rounds.
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.
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. H: Except to the aficionados, who were passing bootlegged copies from mimeo- graph machines. They were extremely hard to find. A: Eventually they were published by MIT Press [v] in ’95, together with ex- tensive postscripts describing what has happened since the late sixties—a tremen- dous 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.
run, you cannot use information without revealing it; you can use information only to the extent that you are willing to reveal it. A player with private information must choose between not making use of that information—and then he doesn’t have to reveal it—or making use of it, and then taking the consequences of the other side finding it out. That’s the big picture. H: In addition, in a non-zero-sum situation, you may want to pass information to the other side; it may be mutually advantageous to reveal your information. The question is how to do it so that you can be trusted, or in technical terms, in a way that is incentive-compatible. A: The bottom line remains similar. In that case you can use the information, not only if you are willing to reveal it, but also if you actually want to reveal it. It may actually have positive value to reveal the information. Then you use it and reveal it. H: You mentioned something else and I want to pick up on that: the Milnor– Shapley paper on oceanic games. That led you to another major work, “Markets with a Continuum of Traders” [16]: modeling perfect competition by a continuum.
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