John F. Nash 's ' A Beautiful Mind ' Mathematician

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Nijatullah Arman
Emma Cummings
22 November 2015
John Nash, 'a Beautiful Mind ' Mathematician

John F. Nash shared the 1994 Nobel Prize with John Harsanyi and Reinhard Selten in economics for their work on the theory of non-cooperative games, in other words John Nash received a Nobel Prize for his work in Game theory. Except for one course in economics that he took as an undergraduate, Nash had not any formal training in economics. John Nash had a Ph.D. in mathematics in 1950, but the Nobel Prize he received four decades later was for the contribution he made to game theory in his 1950 Ph.D. thesis. In his work, he introduced the distinction between cooperative and non-cooperative games. In non-cooperative games every player is self-enforced, and in cooperative games, players can make agreements with other players. Nash’s contribution is the concept of equilibrium for non-cooperative games, which later came to be called a Nash equilibrium. In Nash equilibrium no player can improve his position by choosing a different strategy. Nash explained that as long as mixed strategies are allowed, for a broad class of games, at least one equilibrium exist. Another Nash’s contribution is his reasoning about “the bargaining problem,” before Nash, economist thought the share of gains each of two parties to a bargain received was always indeterminate. But Nash got further by suggesting four conditions and showed mathematically that a unique solution

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