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Playing Games: What John Nash Was Actually Famous
For
As Chariots Of Fire did for Eric Liddell and Braveheart did for
William Wallace, the 2002 film A Beautiful Mind made
mathematician John Forbes Nash a household name - without
necessarily rendering his life, or his work, much
better-understood. Audiences and critics welcomed the movie -
it won a 2004 Academy Award - but enthusiasts of Nash's work
insist that even bigger rewards await those who study Nash's
real-life work, and the esoteric discipline, game theory, in
which he made his name.
Born in Bluefield, West Virginia, in 1928, Nash was already
carrying out bedroom scientific experiments at the age of
twelve. He didn't excel in sports or other stereotypically
youthful pursuits, instead fixing on E.T. Bell's book Men of
Mathematics with the same intensity that a young would-be
guitarist might bring to, say, Led Zeppelin IV. While still in
high school, he took college-level math classes, and a
Westinghouse scholarship to the Carnegie Institute of
Technology (a school known, and revered, today as Carnegie
Mellon) seemed to confirm his vocation as a mathematician - a
vocation only confirmed when Princeton aggressively recruited
him to its Ph.D. program in mathematics. He finished his
doctorate in 1950.
Much of his important early work - including the three
scholarly articles that defined and explained the tendency that
came to be known as "Nash equilibrium" and which (many years
later) helped secure him a 1994 Nobel Prize - had to do with
game theory, a branch of mathematics that analyzes the ways
people interact. Game theorists construct equations that
reflect peoples' assumed motives in entering a situation, and
then analyze the range of possible actions they may take. They
use mathematical modeling to determine what the actual outcomes
of the situation, then, will be.
A logical puzzler known as the Prisoner's Dilemma offers a good
quick example of how basic game theory works. Imagine two
prisoners caught near the scene of a burglary and hauled in by
the police. The cops know that they've found their suspects,
but they can't get either person to admit guilt, so they offer
each man a deal. As Michael A.M. Lerner, writing in Good
Magazine, describes it: "If they both confess and cooperate,
they'll both get a minor sentence of five years. If neither man
confesses, they'll both only get one year - But, and here's
where it gets interesting, if one confesses and the other
doesn't, the one who confesses walks out scot-free while the
other will do 10 years. What will they do? Will they trust each
other and do what's obviously in their best interest, which is
not confess?" Game theorists assume that each person in this
dilemma is out for themselves; assigning values accordingly,
they come up with equations that predict the two burglars will
betray each other - even though it makes more sense to
cooperate.
It may sound crazy - how on earth can something that seems as
cut-and-dry as math make successful, predictive models of how
humans will behave in a real-world situation? But
mathematicians, economists and political scientists have used
game theory to yield some startlingly accurate predictions.
Game theorist Benito de Mesquita used his own equations to
predict the Ayatollah Khomeini's successor, in 1984; when his
answer proved, several years later, to be correct, it launched
a career that now includes a rich consulting firm and several
Pentagon collaborations. Game theory may not be
uncontroversial, but it does look to be here to stay.
Nash's own most famous work has to do with the way we can
assume people will behave in certain "non-cooperative" games,
i.e. situations in which people compete against each other. He
showed, in general, that there are limits on the degree of
success that can be achieved by people in competition against
each other - that, contra Adam Smith (the father of modern
economics), some kinds of competition tend to reduce the amount
of good stuff available for everyone (rather than making the
total size of the pot bigger, as Smith is usually assumed to
have taught). This is the insight for which - decades later,
after his protracted struggle with schizophrenia, and along
with Reinhard Selten and John Harsanyi - he won the Nobel
Prize. It may not be as photogenic as Russell Crowe (who played
Nash in the movie), but it's - who knows? - probably more
relevant to your life.
by Ann Knapp - 16th September 2008
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