On Zero-Sum Two Person Games
Abstract
The field of game theory is a relatively new topic among mathematicians and economist.
It was not until 1944 when John von Neumann and Oskar Morgenstern published the famous book
"Theory of Games and Economic Behavior" was game theory a recognized field. The contributions
of game theory were recognized in 1994 when John Nash, John C. Harsanyi and Reinhard Selten were
awarded the Nobel prize in Economics for their work in game theory. Game theory encompasses
a wide variety of games and situations that can be analyzed using the theoretical models
developed through maximization methods in mathematics. The most basic of these models is the
zero-sum two person game with finitely many strategies. These games can be solved using the minimax theorem.
The minimax theorem was proven by John von Neumann in 1928 in his article "Zur Theorie der Gesellschaftsspiele"
using topology and functional calculus. This theorem has proven to be extremely useful in analyzing
and finding the Nash equilibrium outcome of two-person zero sum games and has acted as spring board
in analyzing more complex games with contant-sum payoffs.
Table of Contents
Complete List of References
- [DA1]
Dixt, Avinash, and Susan Skeath.
Games of Strategy.
New York: Norton & Company, 2004.
- [OG1]
Owen, Guillermo.
Game Theory.
San Diego: Academic Press, 1995
- [RA1]
Rapoport, Anatol.
N-Person Game Theory: Concept and Applications.
Michigan: University of Michigan Press, 1970.
