### Topic Page: Nash, John F. (1928 - 2015)

**Nash, John F(orbes) Jnr**from

*Chambers Biographical Dictionary*

1928-

♦ US mathematician and Nobel Prize winner

Born in Bluefield, West Virginia, he was educated at Carnegie Mellon and Princeton universities and subsequently worked at the Massachusetts Institute of Technology (1951-59). In the late 1950s he developed paranoid schizophrenia and was unable to work for the next two decades, after which time he returned to Princeton. He shared the 1994 Nobel Prize in economics with John C Harsanyi and Reinhard Selten for their pioneering work on game theory, and was awarded the Leroy P Steele Prize in 1999. His biography by Sylvia Nasar, A Beautiful Mind (1998), was made into a film in 2001.

**Nash, John**

*Economic Thinkers: A Biographical Encyclopedia*

Born: June 13, 1928, in Bluefield, West Virginia; American; game theory, Nash equilibrium, mathematics; Major Works: “Equilibrium Points in N-Person Games” (1950), “The Bargaining Problem” (1950), “Non-cooperative Games” (1951), “Two-Person Cooperative Games” (1953).

John Nash is a mathematician who developed advanced studies of game theory that expanded their application to broad categories of political science, economics, business strategy, biology, and personal interactions. In 1994, he was awarded the Nobel Prize in Economics for his work in game theory with John Harsanyi and Reinhard Selten. Nash equilibrium is the most widely used and applied solution concept of game theory. Nash was the subject of the 2002 film A Beautiful Mind, which portrayed his struggle with paranoid schizophrenia.

John Forbes Nash was born on June 13, 1928, in Bluefield, West Virginia. He was raised in a highly intellectual environment and developed advanced mathematical skills as a child. Awarded the coveted George Westinghouse Scholarship, he began his undergraduate studies at Carnegie Institute of Technology (now Carnegie Mellon University) in chemical engineering. He did not care for the regimentation of the engineering classes or the quantitative analysis of the chemistry classes and changed to mathematics.

From an international economics course at Carnegie, he derived the idea for his paper “The Bargaining Problem” and ultimately his interest in game theory. By graduation he had progressed in his studies of mathematics and was awarded an MA degree in addition to the BS degree.

He was offered fellowships to both Harvard University and Princeton University for further studies in mathematics.

He chose Princeton because it was closer to home. During his graduate studies one of his discoveries led to “Noncooperative Games.” He concurrently developed two theses, one in game theory and one based on his discovery relating to manifolds and real algebraic varieties.

His academic career began in 1950 at Princeton where he taught for one year. In 1951, he accepted a higher-paying position as a C.L.E. Moore instructor at the Massachusetts Institute of Technology (MIT) where he remained till 1959. During this time he solved a problem relating to differential geometry as well as developed the theorem known as the Nash embedding theorem.

He accepted the Alfred P. Sloan grant and returned to Princeton as a member of the Institute for Advanced Studies (IAS). While at IAS, he solved a problem involving partial differential equations. Unbeknownst to him, Ennio de Giorgi of Pisa, Italy, was also working on the problem and solved it prior to Nash. Had only one of the men solved this equation, it is speculated that he would have received the famous mathematics Field Medal.

John Nash made important contributions to game theory research. Game theory allows social scientists to evaluate interactive decision making when the outcome for one participant is dependent on the actions or strategies of all other participants. Nash introduced the distinction of identifying cooperative and noncooperative games. Cooperative games allow players to form binding enforceable agreements and make irrevocable threats to other players. Noncooperative games do not allow for such possibilities. The science of game theory can be applied broadly in the areas of experimental economics, behavioral economics, industrial organization, and political economy. Noncooperative games are accurate at understanding and predicting social interactions, voting behaviors, fair division, auction, mergers and acquisitions, corporate compensation plans, bargaining systems, oligopolies, and duopolies. Nash identified the equilibrium point in such games. It is a set of strategies and the corresponding pay-offs when no player may benefit by changing his strategy while other players leave their strategies unchanged.

A player would not choose to change his or her strategy for optimal outcome even after learning the strategies of other players. This is known as Nash equilibrium. Nash equilibrium is the most widely used and applied solution concept of game theory because it yields the most accurate insights into the workings of the social situation to which it is applied. In 1994, John Nash, with John Harsanyi and Reinhard Selten, received the Nobel Memorial Prize in Economic Sciences as a result of his game theory work as a graduate student at Princeton.

John Nash struggled with paranoid schizophrenia beginning in early 1959, which resulted in an involuntary hospital stay, his resignation from MIT, and an attempt to renounce his U.S. citizenship, seeking political asylum in France and East Germany. His experience was portrayed in Sylvia Nasar's 1998 movie A Beautiful Mind. He later spoke out against Nasar's false depiction that he recovered as a result of atypical antipsychotics when in fact he refused any medication after 1970. He credits his recovery to his decision to renounce his delusional hypotheses and to return to rational thought.

In addition to the Nobel Prize in 1994, Nash has been awarded the John von Neumann Theory Prize for his discovery of Nash equilibria (1978) and several honorary degrees and doctorates.

See also: Harsanyi, John; Selten, Reinhard

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