John Nash, immortalized in the book and movie 'A Beautiful Mind,' died on this day in 2015, ending a dramatic story of genius.
, made for drama suitable for a movie. Russell Crowe played Nash in the 2001 film, which garbled the math but made the point that despite his affliction, Nash accomplished works of genius — particularly in the theory of games.
At Princeton, Nash revolutionized economic theory, showing how the freshly developed game theory of the great John von Neumann and Oskar Morgenstern could be made more relevant to real life. In their book,, von Neumann and Morgenstern had attempted to derive a mathematics of strategy. They showed how participants in an economy could choose the most profitable behaviors.
Out of this work came the concept of the “Nash equilibrium,” the set of strategies that guaranteed the best possible payoff for all participants. Nash’s genius was to prove that at least one such set of strategies was always possible. In other words, as the economist Samuel Bowles once put it, there is always “a situation in which everybody is doing the best they can, given what everybody else is doing.
Nash’s equilibrium became the bedrock upon which game theory’s future was built. “The concept of the Nash equilibrium is probably the single most fundamental concept in game theory,” Bowles said. And the economist Roger Myerson called it “one of the outstanding intellectual advances of the 20th century … comparable to that of the discovery of the DNA double helix.”
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