SAT寫作經典例子

　　Key words: economist illness Nobel price winner

　　John Nash

　　When the young Nash had applied to graduate school at Princeton in 1948, his old Carnegie Tech professor, R.J. Duffin, wrote only one line on his letter of recommendation: This man is a genius.

　　It was at Princeton that Nash encountered the theory of games, then recently launched by John von Neumann and Oskar Morgenstern. However, they had only managed to solve non-cooperative games in the case of pure rivalries . The young Nash turned to rivalries with mutual gain. His trick was the use of best-response functions and a recent theorem that had just emerged - Kakutanis fixed point-theorem.

　　His main result, the Nash Equilibrium, was published in 1950 in the Proceedings of the National Academy of Sciences. He followed this up with a paper which introduced yet another solution concept - this time for two-person cooperative games - the Nash Bargaining Solution in 1950. A 1951 paper attached his name to yet another side of economics - this time, the Nash Programme, reflecting his methodological call for the reduction of all cooperative games into a non-cooperative framework.

　　His contributions to mathematics were no less remarkable. As an undergraduate, he had inadvertently proved Brouwers fixed point theorem. Later on, he went on to break one of Riemanns most perplexing mathematical conundrums. From then on, Nash provided breakthrough after breakthrough in mathematics.

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