On Numbers and Games

The book On a New Arithmetic of Games, originally written to define the relation between transfinite numbers and mathematical games, 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. 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. 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 partisan games.