Definition:Game Theory

Definition

Game theory is the branch of discrete mathematics which studies mathematical models of conflict and cooperation between intelligent rational decision-makers.

Problems in game theory are a special case of those of linear programming.

Historical Note

The origins of the mathematical discipline of game theory can be traced to Ernst Zermelo's 1913: Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels ("On an Application of Set Theory to the Theory of the Game of Chess") (Proceedings of the Fifth International Congress of Mathematicians Vol. 2: pp. 501 – 504).

Another early landmark was Émile Borel's 1921: La Théorie du Jeu et les Équations Intégrales à Noyau Symétrique (C.R. Acad. Sci. Vol. 173: pp. 1304 – 1308).

He also stated, but failed to prove, a special case of the Fundamental Theorem of Games in his paper of 1927: Sur les systèmes de formes linéaires à déterminant symétrique gauche et la théorie générale du jeu (C.R. Acad. Sci. Vol. 184: pp. 52 – 54).

The proof was given in a lecture by John von Neumann, documented as 1928: Zur Theorie der Gesellschaftspiele (Math. Ann. Vol. 100: pp. 295 – 320).

The field was properly established by John von Neumann and Oskar Morgenstern in their Theory of Games and Economic Behaviour of $1944$, as a result of their observation that certain problems in economics were identical with those of games of strategy.

As the field evolved, it became apparent that this new discipline had a considerable number of wide-ranging applications.

Also see

• Results about game theory can be found here.