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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.
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 ...
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.
Game theory is applied (for a change) to games 1968 Jan: The beauties of the square, as expounded by Dr. Matrix to rehabilitate the hippie 1968 Feb: Combinatorial problems involving tree graphs and forests of trees 1968 Mar: A short treatise on the useless elegance of perfect numbers and amicable pairs: 1968 Apr: Puzzles and tricks with a ...
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.
Combinatorial game theory is a branch of mathematics and theoretical computer science ... was Conway's 1976 book On Numbers and Games, ... number of free moves, or ...
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.
The Grundy value or nim-value of any impartial game is the unique nimber that the game is equivalent to. In the case of a game whose positions are indexed by the natural numbers (like nim itself, which is indexed by its heap sizes), the sequence of nimbers for successive positions of the game is called the nim-sequence of the game.