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Game theory in the popular press.

The tortured genius behind game theory

Review of A Beautiful Mind

Michael J. Mandel
July 1, 1998
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In 1950, at the age of 22, John Forbes Nash Jr. created modern game theory with two brilliant papers. In 1959, shortly after being granted tenure in the mathematics department at the Massachusetts Institute of Technology, he was involuntarily committed to McLean Hospital in Belmont, Mass., with a diagnosis of paranoid schizophrenia. He left MIT, driven by voices and visions, and for the next 30 years languished in obscurity. In 1994, however, Nash was awarded the Nobel Memorial Prize in Economic Science as a result of his youthful work on game theory.

In A Beautiful Mind, Sylvia Nasar, an economics correspondent for The New York Times, tells the story of Nash's roller-coaster ride up to the heights of mathematical prowess, down through madness, and finally out again. The book is a fascinating account of creativity barely under control, of a mathematical genius who was driven by--and eventually overwhelmed by--his own inner demons. It represents a staggering feat of writing and reporting, and includes an unprecedented look at the inner workings of the Nobel prize committee.

But the best intellectual biographies explore ideas as well as people, and that's where Nasar falls short. Missing here is any discussion of how game theory--which tries to offer a comprehensive explanation of how individuals, corporations, and governments make strategic choices--fits into economics, other than a repeated and unsupported assertion of its importance.

Even without that intellectual framework, A Beautiful Mind is a vivid portrait of the world of top-level mathematics in postwar America. Nasar lavishes most of her attention on the years of Nash's development, from his awkward undergraduate life at the Carnegie Institute of Technology to his short-lived tenured position at MIT. She deftly lays out his self-centered, arrogant personality, which made him a hard person to be around but also enabled him to attack difficult mathematical problems without flinching.

In the space of a few years, Nash gained a reputation as one of the best mathematicians of his generation. He also fathered a child out of wedlock, got arrested for indecent exposure in a men's rest room (which, in that era of intense homophobia, resulted in his being kicked out of RAND Corp. as a security risk), and married a beautiful MIT physics student who, despite having later divorced him, continued to take care of him during his decades of infirmity.

Nasar gives an eloquent account of Nash's struggle with paranoid schizophrenia. By the summer of 1960, he was roaming the streets of Princeton, N.J., where he was then living. ''With dark hair to his shoulders and a busy black beard, he had a fixed expression, a dead gaze,'' writes Nasar. ''Women, especially, found him frightening.''

By 1970, after several stays in mental institutions, Nash had calmed down somewhat. Having returned to Princeton, where he was looked after by his ex-wife and protected by a few friendly mathematicians, he became known as the ''Phantom of Fine Hall,'' the building in which Princeton's mathematics department was located. Nash would leave cryptic messages and equations on classroom and hallway blackboards, and he spent countless hours in the Princeton library.

Despite the increasing prominence of his early work, Nash was effectively invisible and forgotten during this period. Indeed, the book opens a window upon how society treats the mentally ill. During the 1980s, in fact, there were several honors that he would have received, says Nasar, if he had not been deemed insane.

But over a period of time, Nash recovered his lucidity. By the late 1980s, when the Nobel committee started considering awarding a prize for game theory, Nash was well enough to be at the top of the list of potential recipients. Still, there was enormous opposition within the committee, based on skepticism about the usefulness of game theory and worries about Nash's state of mind.

And even though the Nobel prize committee eventually voted in favor of giving the award to Nash, the fight was not yet over. On the day the winner of the prize is announced, the Royal Swedish Academy of Sciences has to vote to approve it. Almost always, the vote is purely a matter of form. But on this occasion, according to Nasar, the nominees were attacked for being ''too narrow, too insubstantial, too technical.'' In the end, writes Nasar, ''Nash and the two other candidates for the 1994 economics prize passed by a mere handful of votes--the first in history to skirt so close to defeat.''

The closeness of the vote also exposed the hostility felt by natural scientists and mathematicians toward the economics prize. They doubted the rigor of the discipline and worried that ''the shallowness of the field [of economics] was leading to a sharp and rapid decline in the quality of Laureates.'' The turmoil over Nash's Nobel prize, according to Nasar, helped prod the Academy in February, 1995, secretly to redefine the economics award ''as a prize in social sciences, open to great contributions in fields like political science, psychology, and sociology.''

Despite her reporting strength, Nasar is sometimes prone to hyperbole. She writes that ''Princeton in 1948 was to mathematicians what Paris once was to painters and novelists...and ancient Athens to philosophers and playwrights.'' The chairman of Princeton's math department, Solomon Lefschetz, becomes ''the supercharged human locomotive that had pulled the Princeton department out of genteel mediocrity right to the top.'' Another Princeton mathematician is described as ''charismatic'' and ''elegant.''

More worrisome, Nasar substantially exaggerates the role of game theory in economics. In an effort to inflate the importance of her subject, she called Nash's theory ''one of the most influential ideas of the twentieth century, transforming the young science of economics the way that Mendel's idea of genetic transmission, Darwin's model of natural selection, and Newton's celestial mechanics reshaped biology and physics in their day.''

Unfortunately, game theory has been a major disappointment. Nash's work did not become the new foundation of economics. There was enormous initial enthusiasm, but game theory was moribund by the 1960s, as its lack of predictive power became clear. And despite a revival of game theory in the 1980s, it was crucial for only a few selected problems, such as analyzing oligopolies, where there are a small number of companies plotting against one another.

Moreover, Nasar mentions but never develops the fascinating notion that modern game theory was invented by a paranoid schizophrenic. ''Nash tended to think of people as out of touch with one another and acting on their own,'' writes Nasar. Little wonder that game theory assumes little or no communication between individuals and no possibility of empathy or cooperation that is not backed by threats. But most experiments to test Nash's theories find that people give substantial weight to principles of fairness rather than simply to self-interest.

Indeed, Nasar devotes very little space to discussion of economic issues. The only application of game theory she explains at length is its use in the recent government auctions of the radio spectrum. And oddly enough, there are relatively few mentions of other economists until page 354--and this in a book about the winner of a Nobel prize in economics.

In many ways, Nasar reflects the attitude of her subject, who cared a lot more about his status as a mathematician than as an economist. In the end, the portrait of Nash is true--and well worth reading.

Copyright 1998, by The McGraw-Hill Companies Inc. All rights reserved.