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The first volume introduces combinatorial game theory and its foundation in the surreal numbers; partizan and impartial games; Sprague–Grundy theory and misère games. The second volume applies the theorems of the first volume to many games, including nim , sprouts , dots and boxes , Sylver coinage , philosopher's phutball , fox and geese .
The Mathematics of Games and Gambling is a book on probability theory and its application to games of chance. It was written by Edward Packel, and published in 1981 by the Mathematical Association of America as volume 28 of their New Mathematical Library series, with a second edition in 2006.
Theory of Games and Economic Behavior, published in 1944 [1] by Princeton University Press, is a book by mathematician John von Neumann and economist Oskar Morgenstern which is considered the groundbreaking text that created the interdisciplinary research field of game theory.
Separately, game theory has played a role in online algorithms; in particular, the k-server problem, which has in the past been referred to as games with moving costs and request-answer games. [125] Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms , especially online ...
It should only contain pages that are Books about game theory or lists of Books about game theory, as well as subcategories containing those things (themselves set categories). Topics about Books about game theory in general should be placed in relevant topic categories .
Conway contributed to combinatorial game theory (CGT), a theory of partisan games. He developed the theory with Elwyn Berlekamp and Richard Guy, and also co-authored the book Winning Ways for your Mathematical Plays with them. He also wrote On Numbers and Games (ONAG) which lays out the mathematical foundations of CGT.
Zermelo's theorem can be applied to all finite-stage two-player games with complete information and alternating moves. The game must satisfy the following criteria: there are two players in the game; the game is of perfect information; the board game is finite; the two players can take alternate turns; and there is no chance element present.
For the purposes of the Sprague–Grundy theorem, a game is a two-player sequential game of perfect information satisfying the ending condition (all games come to an end: there are no infinite lines of play) and the normal play condition (a player who cannot move loses).