Siegfried, Tom. "3 Nash’s Equilibrium--Game theory’s foundation." A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature. Washington, DC: The National Academies Press, 2006.
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A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature
molecules. When people are involved, all sorts of new sources of unpredictability complicate the game theory playing field. (Imagine how much trickier chemistry would become if molecules could think.18)
Nevertheless, Nash’s notion of equilibrium captures a critical feature of the social world. Using Nash’s math, you can figure out how people could reach stability in a social situation by comparing that situation to an appropriate game. So if you want to apply game theory to real life, you need to devise a game that captures the essential features of the real-life situation you’re interested in. And life, if you haven’t noticed, poses all sorts of different circumstances to cope with.
Consequently game theorists have invented more games than you can buy at Toys R Us. Peruse the game theory literature, and you’ll find the matching pennies game, the game of chicken, public goods games, and the battle of the sexes. There’s the stag hunt game, the ultimatum game, and the “so long sucker” game. And hundreds of others. But by far the most famous of all such games is a diabolical scenario known as the Prisoner’s Dilemma.
TO RAT OR NOT TO RAT
As in all my books, a key point has once again been anticipated by Edgar Allan Poe. In “The Mystery of Marie Roget,” Poe described a murder believed by Detective Dupin to have been committed by a gang. Dupin’s strategy is to offer immunity to the first member of the gang to come forward and confess. “Each one of a gang, so placed, is not so much … anxious for escape, as fearful of betrayal,” Poe’s detective reasoned. “He betrays eagerly and early that he may not himself be betrayed.”19 It’s too bad that Poe (who was in fact a trained mathematician) had not thought to work out the math of betrayal—he might have invented game theory a century early.
As it happened, the Prisoner’s Dilemma in game theory was first described by Nash’s Princeton professor, Albert W. Tucker, in 1950. At that time, Tucker was visiting Stanford and had men-