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Nash recovered from his devastating illness, defying a common misconception about schizophrenia and providing the inspiration for Ron Howard's 2002 Oscar-winning film "A Beautiful Mind," starring Russell Crowe.
Nash's Nobel was for a concept he laid out in his doctoral thesis when he was just 21.
The paper was only 27 pages - and "very generously double-spaced," his friend and Princeton colleague Harold W. Kuhn joked to a Nobel seminar in 1994.
But the implications of what came to be called "the Nash equilibrium" were huge.
"Nash's insight into the dynamics of human rivalry - his theory of rational conflict and cooperation - was to become one of the most influential ideas of the twentieth century," his biographer Sylvia Nasar wrote in her 1999 book "A Beautiful Mind."
Nash transformed economics, Nasar wrote, just as "Mendel's ideas of genetic transmission, Darwin's model of natural selection, and Newton's celestial mechanics reshaped biology and physics in their day."
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Crowe said he was "stunned" at hearing about Nash's death.
"My heart goes out to John & Alicia & family. An amazing partnership. Beautiful minds, beautiful hearts," he said on Twitter.
Brian Grazer, who produced the film, said on Twitter that he was "incredibly sad to lose the wonderful, intelligent miracle of John Nash and his wife. (hashtag)ABeautifulMind was the gift of a lifetime."
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"John's remarkable achievements inspired generations of mathematicians, economists and scientists who were influenced by his brilliant, groundbreaking work in game theory," said Christopher L. Eisgruber, president of Princeton University.
Nash worked at Princeton.
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