What is Game Theory?
1. Interdisciplinary approach to the study of human behavior.
2. The disciplines most involved in game theory are mathematics, economics and the
other social and behavioral sciences.
http://william-king.www.drexel.edu/top/eco/game/game.html
A Time Line Taken From: http://williamking.www.drexel.edu/top/class/histf.html#AT
1. Babylonian Marriage contract problem In 1985, it was recognized that the
Talmud anticipates the modern theory of cooperative games.
2. 1913
The first theorem of game theory asserts that chess is strictly determined, ie: chess
has only one individually rational payoff profile in pure strategies. This theorem
was published by E. Zermelo in his paper Uber eine Anwendung der Mengenlehre
auf die Theorie des Schachspiels and hence is referred to as Zermelo's Theorem.
3. 1921-27 Emile Borel published four notes on strategic games and an erratum to
one of them.
4. 1928
John von Neumann proved the minimax theorem in his article Zur Theorie der
Gesellschaftsspiele.
5. 1944 Theory of Games and Economic Behavior by John von Neumann and Oskar
Morgenstern is published.
6. 1950 In January 1950 Melvin Dresher and Merrill Flood carry out, at the Rand
Corporation, the experiment which introduced the game now known as the
Prisoner's Dilemma.
7. 1950-53 In four papers between 1950 and 1953 John Nash made seminal
contributions to both non-cooperative game theory and to bargaining theory. In
two papers, Equilibrium Points in N- Person Games (1950) and Non-cooperative
Games (1951)
8. 1954 One of the earliest applications of game theory to political science is L. S.
Shapley and M. Shubik with their paper A Method for Evaluating the Distribution
of Power in a Committee System.
9. 1955 One of the first applications of game theory to philosophy is R. B.
Braithwaite's Theory of Games as a Tool for the Moral Philosopher.
10. 1982 Publication of Evolution and the Theory of Games by John Maynard
Smith.1989
11. The journal Games and Economic Behavior founded.
John Nash: Excerpts from: http://www-gap.dcs.stand.ac.uk/~history/Mathematicians/Nash.html
1. He seems to have shown a lot of interest in books when he was young but little
interest in playing with other children.
2. His mother responded by enthusiastically encouraging Johnny's education, both
by seeing that he got good schooling and also by teaching him herself. Johnny's
father responded by treating him like an adult, giving him science books when
other parents might give their children colouring books.
3. Johnny was always different. [My parents] knew he was different. And they knew
he was bright. He always wanted to do thinks his way. Mother insisted I do things
for him, that I include him in my friendships. ... but I wasn't too keen on showing
off my somewhat odd brother.
4. he continued to conduct his own chemistry experiments and was involved in
making explosives which led to the death of one of his fellow pupils. [2]:Boredom and simmering adolescent aggression led him to play pranks, occasionally ones
with a nasty edge
5. Nash won a scholarship in the George Westinghouse Competition and was
accepted by the Carnegie Institute of Technology (now Carnegie-Mellon
University)
6. We tormented poor John. We were very unkind. We were obnoxious. We sensed
he had a mental problem.
7. He showed homosexual tendencies, climbing into bed with the other boys who
reacted by making fun of the fact that he was attracted to boys and humiliated
him. They played cruel pranks on him and he reacted by asking his fellow
students to challenge him with mathematics problems. He ended up doing the
homework of many of the students.
8. When Lefschetz offered him the most prestigious Fellowship that Princeton had,
Nash made his decision to study there.
9. In 1949, while studying for his doctorate, he wrote a paper which 45 years later
was to win a Nobel prize for economics.
10. A lot of us would discount what Nash said. ... I wouldn't want to listen. You didn't
feel comfortable with the person.
11. He had ideas and was very sure they were important. He went to see Einstein not
long after he arrived in Princeton and told him about an idea he had regarding
gravity. After explaining complicated mathematics to Einstein for about an hour,
Einstein advised him to go and learn more physics. Apparently a physicist did
publish a similar idea some years later.
12. There's no significant news from here, as always. Martin is appointing John Nash
to an Assistant Professorship (not the Nash at Illinois, the one out of Princeton by
Steenrod) and I'm pretty annoyed at that. Nash is a childish bright guy who wants
to be "basically original," which I suppose is fine for those who have some basic
originality in them. He also makes a damned fool of himself in various ways
contrary to this philosophy. He recently heard of the unsolved problem about
imbedding a Riemannian manifold isometrically in Euclidean space, felt that this
was his sort of thing, provided the problem were sufficiently worthwhile to justify
his efforts; so he proceeded to write to everyone in the math society to cheek on
that, was told that it probably was, and proceeded to announce that he had solved
it, module details, and told Mackey he would like to talk about it at the Harvard
colloquium. Meanwhile he went to Levinson to inquire about a differential
equation that intervened and Levinson says it is a system of partial differential
equations and if he could only [get] to the essentially simpler analog of a single
ordinary differential equation it would be a damned good paper - and Nash had
only the vaguest notions about the whole thing. So it is generally conceded he is
getting nowhere and making an even bigger ass of himself than he has been
previously supposed by those with less insight than myself. But we've got him and
saved ourselves the possibility of having gotten a real mathematician. He's a
bright guy but conceited as Hell, childish as Wiener, hasty as X, obstreperous as
Y, for arbitrary X and Y.
13. He met Eleanor Stier and they had a son, John David Stier, who was born on 19
June 1953. Eleanor was a shy girl, lacking confidence, a little afraid of men, didn't
want to be involved. She found in Nash someone who was even less experienced
than she was and found that attractive. [2]:-
14. One of Nash's students at MIT, Alicia Larde, became friendly with him and by the
summer of 1955 they were seeing each other regularly. He also had a special
friendship with a male graduate student at this time Jack Bricker. Eleanor found
out about Alicia in the spring of 1956 when she came to Nash's house and found
him in bed with Alicia.
15. Nash was awarded (jointly with Harsanyi and Selten) the 1994 Nobel Prize in
Economic Science for his work on game theory.
The Prisoner’s Dilemma