Like Chariots Of Fire for Eric Liddell and Braveheart for William Wallace, the 2002 film A Beautiful Mind made mathematician John Forbes Nash a household name, without necessarily making his life or work any better understood. Audiences and critics welcomed the film, which won an Academy Award in 2004, but fans of Nash’s work insist that even greater rewards await those who study Nash’s real-life work and discipline. esoteric, game theory, in which he became famous.
Born in Bluefield, West Virginia, in 1928, Nash was already conducting bedroom science experiments at the age of twelve. He didn’t excel at sports or other stereotypically boyish activities, instead focusing on ET Bell’s Men of Mathematics with the same intensity that a young aspiring guitarist might bring to, say, Led Zeppelin IV. While still in high school, he took college-level math classes, and a Westinghouse Fellowship 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 that was only confirmed when Princeton aggressively recruited him for its Ph.D. program in mathematics. He finished his doctorate in 1950.
Much of his important early work, including the three scholarly papers that defined and explained the trend that came to be known as the “Nash equilibrium” and (many years later) helped win the 1994 Nobel Prize, had to do with the games theory. a branch of mathematics that analyzes the ways in which people interact. Game theorists build equations that reflect people’s presumed motives for entering a situation, and then analyze the range of possible actions they can take. They use mathematical models to determine what the actual results of the situation will be.
A logic puzzle known as the Prisoner’s Dilemma offers a good quick example of how basic game theory works. Imagine two prisoners trapped near the scene of a robbery and detained by the police. The cops know they’ve found their suspects, but can’t get either man to admit guilt, so they offer each man a deal. As Michael AM Lerner describes it, writing in Good Magazine: “If they both confess and cooperate, they will both receive a less than five year sentence. If neither confesses, they will both receive only one year, but, and this is where it gets interesting. If one confesses and the other does not, the one who confesses gets away with it while the other will serve 10 years. Interest, what is not confessing?” Game theorists assume that each person in this dilemma is outside of themselves; assigning values accordingly, they come up with equations that predict that the two thieves will betray each other, even though it makes more sense to cooperate.
It may sound crazy: how the heck can something that seems as simple as mathematics 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 produce some surprisingly accurate predictions. Game theorist Benito de Mesquita used his own equations to predict the successor to Ayatollah Khomeini, in 1984; when his answer turned out to be correct several years later, he launched a career that now includes a wealthy consulting firm and various Pentagon collaborations. Game theory may not be without controversy, but it seems to be here to stay.
Nash’s most famous work has to do with the way in which we can assume that people will behave in certain “non-cooperative” games, that is, situations in which people compete with each other. He showed, in general, that there are limits to the degree of success that people can achieve in competition with each other; that, contrary to Adam Smith (the father of modern economics), some kinds of competition tend to reduce the amount of good stuff available to everyone (instead of making the overall size of the pot bigger, as Smith is supposed to have taught ). This is the idea for which, decades later, after his long fight against schizophrenia, and together with Reinhard Selten and John Harsanyi, he won the Nobel Prize. He may not be as photogenic as Russell Crowe (who played Nash in the movie), but he is, who knows? – probably more relevant to your life.