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## Playing Games – What John Nash Was Actually Famous For

Just 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 making his life or work were much better understood. The film was well received by audiences and critics – it won an Academy Award in 2004 – but enthusiasts of Nash’s work insist that those who study Nash’s real-life work and discipline esoteric game theory, in which he made his name, expect even greater rewards.

Born in Bluefield, West Virginia, in 1928, Nash was already conducting science experiments in his bedroom at the age of twelve. He didn’t excel at sports or other stereotypically youthful pursuits, instead fixating on ET Bell’s book 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 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 calling only confirmed when Princeton aggressively recruited him for his Ph.D. math program He finished his doctorate in 1950.

Much of his early important work—including the three academic papers that defined and explained the trend that became known as “Nash equilibrium” and that (many years later) helped him win the 1994 Nobel Prize—had to do with game theory, a branch of mathematics that analyzes the way people interact. Game theorists construct equations that reflect people’s assumed motives for entering a situation, and then analyze the range of possible actions they might take. They use mathematical models to determine what the actual outcomes of the situation will be.

A logic puzzle known as the Prisoner’s Dilemma provides a good quick example of how basic game theory works. Imagine two prisoners caught near the scene of a robbery and dragged away by the police. The cops know they’ve found their suspects, but they can’t get either man to admit guilt, so they offer each man a deal. As Michael AM Lerner, writing in Good Magazine, describes it: “If both men confess and cooperate, they will both get a sentence of less than five years. If neither man confesses, they will both get only one year, however, and here’s it gets interesting, if one confesses and the other doesn’t, the one who confesses gets away with nothing while the other does 10 years. What will they do? They will trust each other and do what is obviously in their best interest moment. interest, which is not confessing?” Game theorists assume that each person in this dilemma is on their own; 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 can something as seemingly 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 surprisingly accurate predictions. Game theorist Benito de Mesquita used his own equations to predict Ayatollah Khomeini’s successor in 1984; when his answer proved correct several years later, he launched a career that now includes a wealthy consulting firm and several Pentagon partnerships. Game theory may not be moot, but it looks like it’s here to stay.

Nash’s most famous work has to do with how 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, against Adam Smith (the father of modern economics), some types of competition tend to reduce the amount of good things available to all (rather than increasing the total size of the pot, as Smith is usually supposed to have taught). This is the vision for which – decades later, after his long struggle 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 most relevant to your life.

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