Game Theory

A branch of Mathematics and Logic which 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.

See also Borel Determinacy Theorem, Categorical Game, Checkers, Chess, Decision Theory, Equilibrium Point, Finite Game, Futile Game, Game Expectation, Go, Hi-Q, Impartial Game, Mex, Minimax Theorem, Mixed Strategy, Nash Equilibrium, Nash's Theorem, Nim, Nim-Value, Partisan Game, Payoff Matrix, Peg Solitaire, Perfect Information, Saddle Point (Game), Safe, Sprague-Grundy Function, Strategy, Tactix, Tit-for-Tat, Unsafe, Value, Wythoff's Game, Zero-Sum Game

References

Game Theory

Berlekamp, E. R.; Conway, J. H; and Guy, R. K. Winning Ways, For Your Mathematical Plays, Vol. 1: Games in General. London: Academic Press, 1982.

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.

Dresher, M. The Mathematics of Games of Strategy: Theory and Applications. New York: Dover, 1981.

Eppstein, D. ``Combinatorial Game Theory.'' http://www.ics.uci.edu/~eppstein/cgt/.

Gardner, M. ``Game Theory.'' Ch. 3 in Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, 1978.

Karlin, S. Mathematical Methods and Theory in Games, Programming, and Economics, 2 Vols. Vol. 1: Matrix Games, Programming, and Mathematical Economics. Vol. 2: The Theory of Infinite Games. New York: Dover, 1992.

Kuhn, H. W. (Ed.). Classics in Game Theory. Princeton, NJ: Princeton University Press, 1997.

McKinsey, J. C. C. Introduction to the Theory of Games. New York: McGraw-Hill, 1952.

Neumann, J. von and Morgenstern, O. Theory of Games and Economic Behavior, 3rd ed. New York: Wiley, 1964.

Packel, E. The Mathematics of Games and Gambling. Washington, DC: Math. Assoc. Amer., 1981.

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://william-king.www.drexel.edu/top/class/histf.html.

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