John Nash is a mathematician and economist who developed game theory and the Nash equilibrium. He won the 1994 Nobel Prize in Economics for his work on the Nash equilibrium, which describes a stable state of a system where no participant can benefit by changing their strategy if others' strategies remain unchanged. Nash struggled with schizophrenia for much of his life but made breakthrough contributions to economics and mathematics as a young man at Princeton University.

1. JOHN FORBES NASH, JR.

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. 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. 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. 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. 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. 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. 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. 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>.