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A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature
Before von Neumann first came to America in 1930, he had established himself in Europe as an exceptionally brilliant mathematician, contributing major insights into such topics as logic and set theory, and he lectured at the University of Berlin. But he was not exactly a bookworm. He enjoyed Berlin’s cabaret-style nightlife, and more important for science, he enjoyed poker. He turned his talent for both math and cards into a new paradigm for economics—and in so doing devised mathematical tools that someday may reveal deep similarities underlying his many diverse scientific interests. More than that, he showed how to apply rigorous methods to social questions, not unlike Asimov’s Hari Seldon.
“Von Neumann was a brilliant mathematician whose contributions to other sciences stem from his belief that impartial rules could be found behind human interaction,” writes one commentator. “Accordingly, his work proved crucial in converting mathematics into a key tool to social theory.”1
UTILITY AND STRATEGY
By most accounts, the invention of modern game theory came in a technical paper published by von Neumann in 1928. But the roots of game theory reach much deeper. After all, games are as old as humankind, and from time to time intelligent thinkers had considered how such games could most effectively be played. As a branch of mathematics, though, game theory did not appear in its modern form until the 20th century, with the merger of two rather simple ideas. The first is utility—a measure of what you want; the second is strategy—how to get what you want.
Utility is basically a measure of value, or preference. It’s an idea with a long and complex history, enmeshed in the philosophical doctrine known as utilitarianism. One of the more famous expositors of the idea was Jeremy Bentham, the British social philosopher and legal scholar. Utility, Bentham wrote in 1780, is “that property in any object, whereby it tends to produce benefit, advantage, pleasure, good, or happiness … or … to prevent the happening of mischief, pain, evil, or unhappiness.”2 So to