A rchive Date
[ 23-02-2005 ]
Category
[ International Relations ]
sub-Categoy
[ Mass Media ]
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[http://www.webfin.com/en/home/columnists/majority_interest/column_detail.html/?id=3381
A Beautiful (Mathematician's) Mind
In next week's glitz fit, the movie "A Beautiful Mind" is nominated for eight Oscars, including one for best movie. Given that the mind in question belonged to John Nash, co-winner of the 1994 Nobel Prize for economics, you might think that economists would be puffed up with pride. The truth is somewhat different.
For one thing, Nash was not an economist, but a mathematician. In the early 1950s he extended the reach of the new science of 'game theory' pioneered by the legendary John von Neumann and Oskar Morgenstern. Nash's results were used in many fields, notably cold-war strategy, but they were perhaps most extensively adopted by economic theorists. So, when it was decided that the 1994 prize for economics would commemorate the fiftieth anniversary of game theory's birth, it went to three people who had advanced the field. Nash was one of the co-winners; the other two were genuine economists.
(There is some speculation as to why there is no Nobel Prize for mathematics. One theory has it that Alfred Nobel's girlfriend left him for a mathematician, Gosta Mittag-Leffler, and Nobel never forgot the injury. There are more plausible theories.)
That Nash was not an economist is probably better for the profession's image. Most economists would rather be thought dull than detestable. The movie glosses over some of Nash's rougher points, but the original book by Sylvia Nasar - an exceptionally good book, by the way - shows that Nash, in his path-breaking years, was a bully, a snob, a racist, an egotist and a deadbeat father to a child born out of wedlock. If there were a Nobel Prize for being a cad, Nash easily could have won that one, too.
Nash's work was brilliant, however. His mind was Olympian in both the sprint and the marathon. He could creatively reframe a question in an instant; and he could devote himself for years to solving a single problem. For example, he won his Nobel Prize for his game-theory work, completed in relatively short order to fulfil his PhD requirements and principally a result of reformatting the assumptions of game theory. (Nationalist note: Albert Tucker, the thesis adviser who was critical to Nash's completing the thesis, was a Canadian.) Nash's work on multi-dimensional geometry, on the other hand, was a marathon: it was much more sophisticated than his game-theory work and took years to accomplish.
So, just what was Nash's contribution to game theory, the basis for his Nobel Prize, his major claim to fame and the reason why a movie would be made of his life? To understand, take a step back to Economics 101.
Classical microeconomics is very good at handling situations where there are many buyers and many sellers, where, in effect, no one has very much influence in the market. Game theory, as developed by von Neumann and Morgenstern, looked at the opposite sort of situation, where there were only two participants.
Think of two gas stations on opposite sides of the street. Each has considerable influence in setting the market price: each wants the price to be as high as possible, each knows that a price war could be ruinous and each knows that cutting price is a way to gain market share. How they determine the price for gasoline is a game-theoretic situation: what station A does is dependent on what it thinks station B will do and vice versa.
If you want a more dramatic example, think of the cold war: each superpower knew that how and where it located its strategic weapons would influence how and where the other superpower would locate its strategic weapons. Game-theory reasoning led the U.S.A. to move much of its air power away from Europe because to leave it there would tempt the U.S.S.R. to a decisive, first strike.
With von Neumann and Morgenstern, however, game theory was limited to situations with two players. Nash's contribution was to show that game theory could be used to analyse situations with many players. The famous 'Nash equilibrium' - well, it's famous to economists anyway - was a stable situation where no player benefits by changing his or her position. Importantly, this stable result is not necessarily the optimum result - Adam Smith's classical market solution wrought by an 'invisible hand' - but it is stable.
This is obviously esoteric stuff - Nash's original paper was 27 pages of dense equations and Tucker had to push him to include some concrete example - but it has had many applications. Business strategies, political strategy, even fields in biology have made use of Nash's insight. Still, game theory remains one of the more abstract fields of economics.
Small wonder, then, that economists aren't exactly embracing "A Beautiful Mind" as an 'economic flic'. (The world is still not ready for the wide-screen version of "Keynes: Bloomsbury Man".) Most economists are probably cheering for "The Lord of the Rings" to win the Oscar for best picture: after all, better a dour wizard than a sour wizard.
Tim Whitehead operates an economic consulting firm, Left Bank Economics Inc., near Paris, Ontario.]
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