John Nash

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John Nash

  1. 1. JOHN FORBES NASH, JR.
  2. 2. Who is John Nash? • John Nash is a mathematician and economist who concentrated primarily on game theory and differential geometry • His work in game theory, especially the “Nash equilibrium,” has reshaped modern economic thought • He won the 1994 Nobel Prize in Economics for the Nash equilibrium
  3. 3. His life • Born in 1928, in Bluefield, WV • He was a child prodigy • He created board games and conducted science experiments in his bedroom • Got his PhD at Princeton University in 1950
  4. 4. Game Theory • Game theory is the study of “games,” strategic situations in which a person must make decisions that affect the outcome for both himself and the other players • Game theory is a branch of mathematics, but it obviously applies to economics
  5. 5. The Nash equilibrium • “If each player’s strategy is the best possible considering every other player’s strategy, then the game is in equilibrium, and will not change.” • No player can benefit by unilaterally changing his or her strategy
  6. 6. Nash Equilibrium in Action: The Arms Race Imagine that the US and USSR only had the options to either build more weapons or stop building weapons completely, and that the Arms Race could be simplified into the four outcomes described in the table. USSR Produce more Stop producing weapons weapons US Produce more Option A: US and Option B: US has weapons USSR both have weapons weapons USSR has less weapons Stop producing Option C: USSR has Option D: US and weapons weapons USSR both have less US has less weapons weapons
  7. 7. The Arms Race • Regardless of what the USSR chose to do, it would have been advantageous for the US to build more weapons, and vice versa • Thus, a game structured this way will tend towards Option A
  8. 8. Later Life • In the 1960s, Nash developed schizophrenia • He suffered from it until at least the 1990s • The movie A Beautiful Mind (2001) was based on his life
  9. 9. Bibliography • "A Brief Introduction to Non-Cooperative Game Theory." Rensselaer at Hartford. Rensselaer Polytechnic Institute, 14 Mar. 2001. Web. 22 Sept. 2009. <http://www.rh.edu/~stodder/BE/IntroGameT.htm>. • Barry, P. (2008, November). Nash's math gets more beautiful. Science News, 174(10), 10. Retrieved September 22, 2009, from KidQuest Magazines. • "Game Theory." Stanford Encyclopedia of Philosophy. 25 Jan. 1997. Web. 27 Sept. 2009. <http://plato.stanford.edu/entries/game- theory/>. • Nash, John F. "John F. Nash, Jr.: Autobiography." Nobelprize.org. The Nobel Foundation, 1994. Web. 22 Sept. 2009. • Kuhn, H. W., and S. Nasar, eds. The Essential John Nash. Princeton, NJ: Princeton UP, 2001. • Wright, Robert. "Nash Equilibrium." Slate. Newsweek Interactive Co., 22 Mar. 2002. Web. 27 Sept. 2009. <www.slate.com>.

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