On Numbers and Games

2000/12/11 by John H. Conway · 1 voice · 14 citations
Decision Sciences · #Game Theory and Applications

paper · doi:10.1201/9781439864159

openalex publication_date 2000/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

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 that includes both real numbers and ordinal numbers: surreal numbers. The second edition presents developments in mathematical game theory, focusing on surreal numbers and the additive theory of partizan games.

Cited by

• An algebraic (set) theory of surreal numbers, I
• On the Sprague-Grundy function of compound games
• The Combinatorial Game Theory of Well-Tempered Scoring Games
• Fractal Sequences and Restricted Nim
• Comparing Distance Bounding Protocols: a Critical Mission Supported by Decision Theory
• Recursive definitions on surreal numbers
• The structure and classification of misère quotients
• Six Lectures on Transseries, Analysable Functions and the Constructive Proof of Dulac’s Conjecture
• Introduction to computability logic
• The Rise of non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of non-Archimedean Systems of Magnitudes
• THE ITERATIVE CONCEPTION OF SET
• Impartial Scoring Play Games
• Cumulative Games: Who is the current player?
• The mathematical role of (commutative and noncommutative) infinitesimal random walks over (commutative and noncommutative) riemannian manifolds in Quantum Physics
• Survey on fusible numbers

Discussions

• Looks like Dedekind cuts/Conway games, I wonder if there’s any insight there doi.org/10.1201/9781... [bsky, 0 points, 0 comments]