On Numbers and Games

This book, defined, if not created, the field of mathematical game theory when it was introduced 25 years ago. In it Conway (mathematics, Princeton U.) explores the strengths of various positions in several games and arrives at a new class of numbers, called surreal numbers, which include both real numbers and ordinal numbers; these surreal numbers are applied in the author's mathematical analysis of game strategies. This new edition has been supplemented with new developments in game theory and a concentration on the additive theory of partizan games. Annotation c. Book News, Inc., Portland, OR (booknews.com)
ONAG, as the book is commonly known, is one of those rare publications that sprang to life in a moment of creative energy and has remained influential for over a quarter of a century. Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently enjoyable guide to game theory. By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers, that includes both real numbers and ordinal numbers. These surreal numbers are applied in the author's mathematical analysis of game strategies. The additions to the Second Edition present recent developments in the area of mathematical game theory, with a concentration on surreal numbers and the additive theory of partizan games.