Game Theory

Game theory is a branch of mathematics that deals with the analysis of games (i.e., situations involving parties with conflicting interests). In addition to the mathematical elegance and complete "solution" which is possible for simple games, the principles of game theory also find applications to complicated games such as cards, checkers, and chess, as well as real-world problems as diverse as economics, property division, politics, and warfare.

Game theory has two distinct branches: combinatorial game theory and classical game theory.

Combinatorial game theory covers two-player games of perfect knowledge such as go, chess, or checkers. Notably, combinatorial games have no chance element, and players take turns.

In classical game theory, players move, bet, or strategize simultaneously. Both hidden information and chance elements are frequent features in this branch of game theory, which is also a branch of economics.

The Season 1 episode "Dirty Bomb" (2005) of the television crime drama NUMB3RS (as well as a number of other episodes) feature character Charlie's use of game theory as a tool for solving crimes.

REFERENCES:

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Berlekamp, E. R.; Conway, J. H; and Guy, R. K. Winning Ways for Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, 1982.

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Mérö, L. Moral Calculations: Game Theory, Logic and Human Frailty. New York: Springer-Verlag, 1998.

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Packel, E. The Mathematics of Games and Gambling, 2nd ed. Washington, DC: Math. Assoc. Amer., 2006.

Stahl, S. A Gentle Introduction to Game Theory. Providence, RI: Amer. Math. Soc., 1999.

Straffin, P. D. Jr. Game Theory and Strategy. Washington, DC: Math. Assoc. Amer., 1993.

Vajda, S. Mathematical Games and How to Play Them. New York: Routledge, 1992.

Walker, P. "An Outline of the History of Game Theory." http://www.econ.canterbury.ac.nz/personal_pages/paul_walker/gt/hist.htm.

Weisstein, E. W. "Books about Game Theory." http://www.ericweisstein.com/encyclopedias/books/GameTheory.html.

Williams, J. D. The Compleat Strategyst, Being a Primer on the Theory of Games of Strategy. New York: Dover, 1986.