John Nash is dead, game theory is still alive – The World

Le Monde | 25/05/2015 at 6:45 • Updated 25/05/2015 to 7:43 | By Hervé Morin

The American mathematician John Nash, who died Saturday, May 23 at age 86 in a car accident when he had just received the Abel Prize in mathematics, was awarded the Nobel Prize in Economics in 1994 for his contributions to game theory. It has become a powerful tool in many disciplines where one seeks to define optimal rational choices – in psychology, political science, geostrategy, ecology …. Game theory had its boom in the 1940s with the work of John von Neumann and Oskar Morgenstern, who at first an interest situations two players, zero sum – where the gain of one is the loss of the other.

Albert Tucker (1905-1995) proposed in 1950 a type of non-zero sum game under the name of the prisoner dilemma, which has seen many variations. One of them up two thugs in the position to denounce his accomplice in exchange for a more lenient sentence, unable to communicate. If both remain silent, thieves will suffer five years in prison. Whoever denounces only have a year to serve. But if it is denounced, it will be ten years. Individual optimum is found that is different from the collective optimum, since to reduce its holding by denouncing his accomplice rational choice, the prisoner is liable to the same penalty since his accomplice may do the same. “It was a very interesting result in economy, which went against the invisible hand of Adam Smith” , says the mathematician Ivar Ekeland (University Paris-Dauphine).

Nash, who was doing his PhD under the direction of Tucker, proposed the same year the concept of balance to reflect game situations pitting any number of players, with a non-zero sum, as in the prisoner’s dilemma. Equilibrium is reached when every player thinks he has conquered a satisfactory position. “Von Neumann was working on a program where game theory would be cooperative with solutions where people could hear” , says Ivar Ekeland. Nash has proposed a non-cooperative solution, individualistic. But as the Von Neumann program was not successful, that of Nash, who represents a kind of “resignation of thought to individualism,” still occupies economists and mathematicians, testifies Ivar Ekeland “because we have not found better” . This particular embodied in the paradoxes of collective action, where solutions that would be beneficial to as many never see the day because their individual rationality fact dam.

morin@lemonde.fr

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