John Nash—one of the great intellectual figures in the development modern game theory—died today in a car crash in New Jersey. According to the New York Times:
John F. Nash Jr., a mathematician who shared a Nobel Prize in 1994 for work that greatly extended the reach and power of modern economic theory and whose decades-long descent into severe mental illness and eventual recovery were the subject of a book and a 2001 film, both titled “A Beautiful Mind,” was killed, along with his wife, in a car crash on Saturday in New Jersey. He was 86.
Dr. Nash was widely regarded as one of the great mathematicians of the 20th century, known for the originality of his thinking and for his fearlessness in wrestling down problems so difficult few others dared tackle them. A one-sentence letter written in support of his application to Princeton’s doctoral program in math said simply, “This man is a genius.”
“John’s remarkable achievements inspired generations of mathematicians, economists and scientists,’’ the president of Princeton, Christopher L. Eisgruber, said, “and the story of his life with Alicia moved millions of readers and moviegoers who marveled at their courage in the face of daunting challenges.”
Russell Crowe, who portrayed Dr. Nash in “A Beautiful Mind,” tweeted that he was “stunned,” by his death. “An amazing partnership,” he wrote. “Beautiful minds, beautiful hearts.”
Dr. Nash’s theory of noncooperative games, published in 1950 and known as Nash equilibrium, provided a conceptually simple but powerful mathematical tool for analyzing a wide range of competitive situations, from corporate rivalries to legislative decision making. Dr. Nash’s approach is now pervasive in economics and throughout the social sciences and is applied routinely in other fields, like evolutionary biology.
Harold W. Kuhn, an emeritus professor of mathematics at Princeton and a longtime friend and colleague of Dr. Nash’s who died in 2014, said, “I think honestly that there have been really not that many great ideas in the 20th century in economics and maybe, among the top 10, his equilibrium would be among them.” An economist, Roger Myerson of the University of Chicago, went further, comparing the impact of Nash equilibrium on economics “to that of the discovery of the DNA double helix in the biological sciences.”
In game theory Nash was particularly known for the Nash equilibrium, a solution in non-cooperative games in which neither player can improve their pay-off by unilaterally changing strategies. In prisoner’s dilemma, for example, an outcome wherein both parties choose to defect forms a stable Nash equilibrium because both are better off by choosing that strategy regardless of what the other party chooses. In this case, however, when parties choose to defect they also fail to obtain the maximum possible payoff (cooperate/cooperate).
video source: Khan Academy
A heavily fictionalized version of John Nash’s life (and his struggles with schizophrenia) were featured in the movie A Beautiful Mind.