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Nash Equilibrium

By Robert WrightPosted Friday, March 22, 2002, at 11:08 AM ET

Last Saturday I had a little chat with John Nash—the tortured genius depicted by Russell Crowe in the movie A Beautiful Mind. I wanted to tie up a loose end in our intertwined histories. It didn't work out quite as I had hoped.

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Though Nash is unaware of this fact, he and I go way back. When I was an undergraduate at Princeton back in the late 1970s, everybody knew who he was, though nobody seemed to know his name. He was just "some math genius who went crazy." He was the middle-aged guy in the colorful sneakers who would sit in Firestone Library or the student center and watch people.

I remember one jarring collision with his gaze. I was in the library and had just had a fleeting social encounter. As the students I was talking to walked away, I looked up and saw Nash staring at me blankly, the way he tended to stare at things. I suddenly had this terrible feeling that he could see to my core—see through whatever pretense I had just put to social use; see through the pretense that pervades social life generally; see that I, and all other noncrazy people, are basically frauds.

Then again, maybe he just thought I was cute. There is, after all, that much-discussed evidence of his homosexual leanings in Sylvia Nasar's book A Beautiful Mind. Still, I do think that mentally ill people sometimes have flashes of unusual insight into the subterranean reality of everyday life. Normal, healthy social functioning requires a certain obliviousness to hidden agendas—our own and sometimes those of others. (As Nash once wrote in another context, "To see this strangeness, the viewer must be strange.")

Anyway, imagine my surprise when, in 1994, 15 years after graduating from Princeton, I opened the New York Times and saw a picture of the math genius who went crazy. He had won a Nobel Prize in economics for his work in game theory.

This was the first I'd heard of his involvement with game theory, something I was getting more and more interested in. Via Robert Axelrod's classic book The Evolution of Cooperation, I had come upon the concept of the "non-zero-sum" game, a game in which there isn't necessarily one winner and one loser, but rather the possibility of two winners—or two losers, depending on whether the players successfully cooperate. (Axelrod mentions the "Nash Equilibrium" in passing, but I hadn't made the connection—since, for one thing, I hadn't known Nash's name.)

After reading Axelrod's book, I had gotten fascinated by the idea that relations among nations are growing more non-zero-sum. For example: With nations getting more economically intertwined, their fortunes are more closely correlated, for better and for worse. So too with environmental problems like global warming and ozone depletion and exhaustion of the world's fisheries: Nations adversely affected by these problems will either cooperate to solve them and all win, or fail to solve them and all lose. And so on, in various policy areas—controlling the spread of nuclear and biological weapons, the spread of disease, etc.

It seemed to me that the growing "non-zero-sumness" among nations called for the eventual evolution of global governance—maybe not a single, centralized world government but still an unprecedented amount of institutionalized cooperation and a commensurate surrender of national sovereignty. In the mid 1990s, I got a contract to write a book making this argument and went to work on it. Meanwhile, Nasar's book about Nash came out, and one part of it caught my attention: Nash used to babble about a coming world government and had even tried to give up his American citizenship and become a citizen of the world.

Nash's world-government obsession is typically cited as a sign of his insanity. (It surfaced around the time he declared himself emperor of Antarctica and seems to have involved messianic delusions.) But, naturally, I wondered whether it might have had a rational dimension. Maybe Nash had realized that relations among nations were growing more non-zero-sum and roughly agreed with me about the implications. Maybe my world view had the endorsement of a Nobel laureate! In any event, my book came out in early 2000 under the title Nonzero, complete with a citation of a 1950 paper by Nash on bargaining in non-zero-sum games.

The year after my book came out, I re-entered Nash's geographic orbit. For a combination of professional and personal reasons, my wife and I decided to rent a house in the Princeton area for a year. A few weeks after moving in, I walked into a Princeton coffee shop and there sat Nash, intently writing equations on a huge sheet of paper. I wanted to ask him whether he had ever thought about the game-theoretic argument for world governance, but I didn't dare approach him. By now Nasar's book had won the National Book Critics Circle Award, and the movie version would debut before long, and I didn't want to seem like a stargazer. Besides, he deserved his space.

Months later, I saw Nash again in the same coffee shop a few blocks from a theater where the movie about him was now playing. At the table next to him a man sat down and started reading A Beautiful Mind, apparently oblivious to the fact that Nash was 6 feet away, just as Nash was oblivious to what the man was reading. Again, I didn't approach.

Then last week I was attending a conference called "Science and Ultimate Reality," sponsored by the John Templeton Foundation. Nash wasn't part of the conference, but during a break I spotted him chatting with Freeman Dyson, the eccentric physicist and cosmic speculator. I started to approach, then hesitated. As I deliberated, Nash and Dyson started walking away. I followed at a distance. They walked down a corridor tentatively, as if looking for something or someone. Then, apparently frustrated, they backtracked. I backtracked in back of them. They walked into the main auditorium, where people were taking their seats in preparation for the next session. I followed. By now I was, to any objective observer, a stalker.

Finally, as Dyson was leading Nash across the auditorium, I said, "Dr. Nash?" Nash stopped, turned around, and looked at me. "I was just wondering if you've ever thought about relations among nations in game theoretic terms—whether you think relations have gotten more non-zero-sum over time." He looked down at my name tag and then said, without much expression, that, no, he hadn't thought much about game theory as it applies to international politics.

Then he looked me dead in the eye, as if he had something of true importance to convey. I waited for the message. "I'm looking for the DeWitts," he said. "Do you know the DeWitts?" I said no. He walked off.

I felt let down, but before long I was successfully rationalizing the situation. Maybe, I thought, Nash wasn't being truthful—with me or even with himself. After all, was it really plausible that a man whose career was centered around game theory had never applied it to the newspaper headlines? (As Nasar's book makes clear, the links between game theory and nuclear disarmament, and between nuclear disarmament and the case for world government, were in the air in Nash's circles at mid-century.)

Besides, would Nash's endorsement of my worldview have amounted to vindication anyway? When my book came out, arguing that world governance is the only long-run alternative to world chaos, some people dismissed me as crazy. Did I really need a blurb from a renowned schizophrenic?

The next night I found myself in a hotel in Amelia Island, Fla. I had just laid out my non-zero-sum-centric worldview to business executives at a conference hosted by Information Week magazine. (Info technology is the great mediator of non-zero-sum games, which is why big changes in it shake up the world.) Sitting on my hotel bed, channel-surfing, I happened upon an interview with Ron Howard, director of A Beautiful Mind. He shared something he'd learned while discussing his movie with Nash: There are big chunks of Nash's life, especially during the periods of intense mental illness, that Nash simply doesn't remember.

Well that explains it! Satisfied, I went to bed.

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Robert Wright, a senior fellow at the New America Foundation, is the editor in chief of Bloggingheads.tv and the author of The Moral Animal, Nonzero, and, most recently, The Evolution of God.

COMMENTS

Reader Comments From The Fray:

This is merely to point out some facts missing from Wright's piece. Nash's dissertation on equilibria in n-person games--the work for which the Nobel in economics was awarded him--was a generalization (an important one) of the fundamentals result of the analysis of two-person games by John von Neumann and Oskar Morgenstern in their famous book The Theory of Games and Economic Behavior. In particular, the notions of equilibrium point and of zero-sum game are their inventions. I'm somewhat surprised that Wright does not cite this fact.

At the same time, Nash's stellar reputation among mathematicians does not center on the game theory work which was, as stated, a dissertation and a generalization of a well-known result in an expected direction, notwithstanding the technical difficulties involved. Other work of Nash's is much more important and striking. In particular, he is best known as the creator of the Isometric Embedding Theorem, which shows that arbitrary Riemannian manifolds can be realized, metrically, as submanifolds of Euclidean space. This is a fundamental result in differential geometry, a field far removed from game theory. The Nobel hardly makes up for the fact that Nash was denied a Fields Medal for this work--in retrospect, a defective judgment. The excessive emphasis on the game-theory paper is one of the ironies of Nash's sudden celebrity.

--Norman Levitt, Professor, Rutgers University

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….The chief irony or cluster of ironies is of course that he's now famous for being Russell Crowe, or famous for being schizophrenic, or famous for maybe possibly or maybe not being homosexual. In other words in typical movie fashion he is famous for the peripheral rather than the central, famous for some oddity of his personal life rather than famous for his work. Just as now Iris Murdoch is famous for having Alzheimer's, Lytton Strachey is famous for having an eccentric sex life, T.S. Eliot is famous for having a difficult marriage, C.S. Lewis is famous for marrying a tiresomely spunky Yank, and Elizabeth I is famous for sleeping with the Earl of Leicester. (See Kate Winslet's immortal observation that she's a great fan of Iris Murdoch's, though she's unfortunately too busy to have read any of her books.)

--Kassandra

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Nash's mental illness consisted in part in not being able effectively to relate his internal states to the real world, so it is hardly a surprise that he does not see nor care about the application of game theory, even to economics (for which he got the Nobel.) His ideas were beautiful, but it is for others, like Wright, to make them useful.

Game theory predicts how rational actors will behave in defined situations and as such can offer explanations for their failures to behave in their own best interests, and prescriptions for their doing so in the future. Nash predicts, economists explain, Wright prescribes.

It seems to me that, among all the dynamics which propel world events, some among them involve rational actors assessing situations in order to promote their own interests. To believe that all events can be explained in these terms is a very common fallacy; to deny that game theory is ever an explanation, or that its implications are ever a good prescription, is equally fallacious.

--artointc

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