John Nash

 

nash picture John Forbes Nash not only won the Nobel Prize, but also is a doctor of mathematics, a leading expert on Game Theory, and was a leading expert on the Cold War. Unfortunately, he is most known for his schizophrenia, a perspective reinforced by the recent movie, A Beautiful Mind. Today we meet with the real John Nash:

Q. Tell us about your childhood, and how the way you grew up influenced your later life.

A. I was born in Bluefield, West Virginia in 1928. My mother and father weren't huge math types. My father was an electrical engineer, and my mother an English teacher. Still, we had an encyclopedia that I read and learned from and some other books. When I was in high school I read E.T. Bell's Men of Mathematics, and that inspired me. Then, in college, at Carnegie Institute of Technology [now Carnegie-Mellon University], I got more involved in a wide range of math.

Q. What did you do after college?

A.  I was offered fellowships to Harvard, Princeton, Chicago, and Michigan and my choice was really between Harvard and Princeton. I felt that Harvard was more prestigious and would have wanted to go there, but in the end it was Princeton who made me the better offer. So I went to Princeton, earned a doctorate and solved a few interesting problems while there. After graduation, I was on the faculty at MIT from 1951 through 1959, and did research there as well that turned out to be fairly fruitful. During this time I also married Alicia Larde. However, it was around this time that I began to exhibit symptoms of my schizophrenia.

Q. What types of symptoms? How did this affect you?

A.  I was forced to resign my position at MIT and was in and out of the hospital, sometimes for months at a time. Eventually, I tended to reject this slightly delusional thinking pattern that I had adopted, and went back to what one might consider a 'normal' thinking pattern. I was not necessarily happier that way, though. What made this an even more difficult time was that Alicia was pregnant. Though I had success in my research both when I was mad and when I was not, eventually I felt that my work would be better respected if I thought and acted like a 'normal' person. In the 1990's I recovered, for the most part, but still continued with my research.

Q. What have you been doing since then?

A.  I was awarded the Nobel Prize in Economics in 1994, and after that was given a research post at Princeton University. I continue to research there, and am currently looking into novel uses for the computer. 

Q. Can you explain to me the innovation that won you the Nobel Prize: The Nash Equilibrium, as it came to be called?

A.  Of course. And contrary to popular belief, it isn't very complicated at all. The basic definition of a Nash Equilibrium is the point at which a competitor is pursuing the best possible strategy given the strategies of the other players.  Say, for example, that there are two companies, each with an equal product. They have a choice: sell their product at a low price or sell it at a high price. Assume that if they both sell it at a high price, they will each earn $3 million. If they each sell at a low price they will earn $2 million. If one sells at a high price though, the other company will undercut him, and sell the product for a low price. Then the company with the low prices will earn $4 million and the company with the high prices only $1 million. Therefore, both companies will sell at the low price to avoid being undercut, even though they could both earn more if they agreed to sell at the high price.

Q.  I see. Does that always work?

A.  The game only works that way if the two players can't agree to work together. For instance, if both companies agreed to sell at the higher price, they would do better. But that isn’t usually the way it works out in the real world.

Q. Is there anything that you would like to add, Mr. Nash?

A. Yes, for the millions of people who saw A Beautiful Mind, they mis-explained a Nash Equilibrium, but if you are interested, it's definitely worth learning about.


Works Cited

“#983: John Forbes Nash, Jr..” Engines of Our Ingenuity. By John H. Lienhard. NPR. KUHF-FM, Houston. Fall 1997. Transcript.

Interesting and mostly factual, though somewhat skewed by opinons of the author.

Kosko, Bart. “How Many Blondes Mess Up a Nash Equilibrium?” Editorial. LA Times 13 Feb. 2002: pages unknown.

Great explanation of a Nash Equilibrium, with many examples. Nothing about Nash’s life.

Nash, John Forbes. “John Forbes Nash - Autobiography.” Les Prix Nobel. N.p., 1994.

Extremely useful description of Nash’s life through his own eyes. A bit difficult to understand the math he discusses.

School of Mathematics and Statistics, University of St. Andrews, Scotland. John Forbes Nash. Sept. 2001. 17 Feb. 2002. http://www-history.mcs.st-andrews.ac.uk/history/References/Nash.html

An excellent source for information about Nash’s life, with quotes from him and those who know him. However, it does not explain his math very well.

Universal Studios. A Beautiful Mind - The Nash Equilibrium. http://www.abeautifulmind.com. 20 Feb. 2002. Path: Raw Data; Essay Information; Essay Tutorial.

Extremely useful for learning about the Nash Equilibrium, but worthless to learn any real biographical details.