john nash

JOHN FORBES NASH, JR.

Who is John Nash?

• John Nash is a mathematician and economistwho concentrated primarily on game theoryand differential geometry

• His work in game theory, especially the “Nashequilibrium,” has reshaped modern economicthought

• He won the 1994 Nobel Prize in Economicsfor the Nash equilibrium

His life

• Born in 1928, in Bluefield, WV• He was a child prodigy• He created board games and

conducted science experiments in hisbedroom

• Got his PhD at Princeton University in1950

Game Theory

• Game theory is the study of “games,”strategic situations in which a personmust make decisions that affect theoutcome for both himself and the otherplayers

• Game theory is a branch ofmathematics, but it obviously applies toeconomics

The Nash equilibrium

• “If each player’s strategy is the bestpossible considering every otherplayer’s strategy, then the game is inequilibrium, and will not change.”

• No player can benefit by unilaterallychanging his or her strategy

Nash Equilibrium in Action:The Arms Race

USSR

US

Produce moreweapons

Stop producingweapons

Produce moreweapons

Option A: US andUSSR both haveweapons

Option B: US hasweaponsUSSR has lessweapons

Stop producingweapons

Option C: USSR hasweaponsUS has less weapons

Option D: US andUSSR both have lessweapons

Imagine that the US and USSR only had the options toeither build more weapons or stop building weaponscompletely, and that the Arms Race could be simplifiedinto the four outcomes described in the table.

The Arms Race• Regardless of what the USSR chose to

do, it would have been advantageousfor the US to build more weapons, andvice versa

• Thus, a game structured this way willtend towards Option A

Later Life

• In the 1960s, Nash developedschizophrenia

• He suffered from it until at least the1990s

• The movie A Beautiful Mind (2001) wasbased on his life

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 morebeautiful. 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 InteractiveCo., 22 Mar. 2002. Web. 27 Sept. 2009. <www.slate.com>.