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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—not necessarily because his life, or his work, is very well-understood. Audiences and critics welcomed the film – it won the 2004 Academy Award – but enthusiasts of Nash’s work insist that those who study Nash’s real-life work, and the esoteric discipline in which he made his name, game theory, await even bigger rewards.

Born in Bluefield, West Virginia in 1928, Nash was already conducting bedroom scientific experiments at the age of twelve. He didn’t excel at sports or other stereotypical youth pursuits, but instead fixated on ET Bell’s book Men of Mathematics with the same intensity that a young guitarist might bring to, say, Led Zeppelin IV. While in high school, he took college-level math classes, and took a Westinghouse scholarship to the Carnegie Institute of Technology (a school known, and today known as Carnegie Mellon) that seemed to confirm his vocation as a mathematician—a vocation only confirmed. When Princeton aggressively offered him a Ph.D. program in mathematics. He completed his doctorate in 1950.

Many of his most important early works – including three scholarly articles that defined and explained the phenomenon known as “Nash equilibrium” and which (many years later) helped him secure the 1994 Nobel Prize – were related to game theory, a branch of mathematics that deals with people’s Analyzes ways of interacting. Game theorists construct equations that reflect people’s presumed intentions when entering a situation, and then analyze the range of possible actions they might take. They use mathematical modeling to determine what the actual outcomes of a 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 arrested near the scene of a robbery and taken away by the police. The cops know they’ve found their suspects, but they can’t get anyone to confess to the crime, so they offer each person a deal. Michael A. M. Lerner, writing in Good Magazine, explained it: “If they both confess and cooperate, they’ll both get a lesser sentence of five years. If one person doesn’t confess, they’ll both get only one year—but, and here’s the interesting thing, if one If one confesses and the other doesn’t, the one confessing gets out scot-free and the other will do 10 years. What will they do? Do they trust each other and clearly do what’s in their best interest? Badge, which confession isn’t?” Game theorists assume that each person in this dilemma is out for himself; Assigning values accordingly, they come up with equations that predict whether two thieves will cheat on each other – even though it makes more sense to cooperate.

This may seem crazy – how on earth can something as cut-and-dry as mathematics lead to successful, predictive models of how people will behave in real-world situations? But mathematicians, economists and political scientists have used game theory to make 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 was proven, many years later, to be correct, it launched a career that now includes a wealthy consulting firm and several Pentagon collaborations. Game theory may not be controversial, but it appears to be here to stay.

Nash’s own best-known work deals with the way we can predict how people will behave in certain “non-cooperative” games, i.e. 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 against each other – that, contrary to Adam Smith (the father of modern economics), some forms of competition reduce its amount. Good stuff is available for everyone (rather than making the total size of the pot larger, as Smith generally believed to have taught). It is this insight for which – decades later, after his long struggle with schizophrenia, and with Reinhard Selten and John Hersani – he won the Nobel Prize. It might not be as photogenic as Russell Crowe (who played Nash in the movie), but it – who knows? – probably very relevant to your life.

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