Nash, John F(orbes), Jr (1928– )

US mathematician. Nash's work on game theory, published in a number of papers in the early 1950s, attracted little attention at the time. By the 1970s, however, as game theory moved to the centre of theoretical economics, Nash became almost overnight one of the best-known names in modern economics. He shared the Nobel Prize for Economics in 1994 with Hungarian-born US economist John Harsanyi and German economist Reinhard Selten, for seminal contributions to game theory.

John von Neumann and Oskar Morganstern founded modern game theory in their classic book, Theory of Games and Economic Behavior (1944). But their analysis, ground-breaking as it was, was confined to two-person zero-sum games (where gains equalled losses as in a game of poker between two players). It was Nash in his 1950 PhD dissertation who first generalized the two-person zero-sum game to allow for multiple players and for non-zero arbitrary-sum games. He found an equilibrium point for such a game, which has ever since been called the ‘Nash equilibrium’: each player in the game adopts the strategy that is the best response to the strategies of all the others.

Nash was born in Bluefield, Virginia, earned a BA and MA in mathematics at Carnegie Institute of Technology (now Carnegie Mellon University) in 1948, and then went on to Princeton University to complete his doctoral dissertation in 1950. Joining the department of mathematics at the Massachusetts Institute of Technology (MIT) in 1951, he was forced to resign in 1959 after a mental breakdown. He resided in Princeton for over 30 years in almost total isolation from academic life but enjoyed a miraculous recovery to full activity in the early 1990s.

At first, the Nash equilibrium only dealt with cooperative games in which players collusively coordinate their strategies, but he later generalized even this feature and showed that the Nash equilibrium outcome characterizes many non-cooperative games. In so doing, he gave birth to the modern theory of rational strategic interactions, one that is capable of dealing not just with ‘games’ but with the problems of rivalry between traders in a competitive market.