Description
Book SynopsisIt is wonderful to see advanced combinatorial game theory made accessible. Siegel's expertise and enjoyable writing style make this book a perfect resource for anyone wanting to learn the latest developments and open problems in the field. --Erik Demaine, MIT Aaron Siegel has been the major contributor to Combinatorial Game Theory over the last decade or so. Now, in this authoritative work, he has made the latest results in the theory accessible, so that the subject will achieve the place in mathematics that it deserves. --Richard Guy, University of Calgary Combinatorial game theory is the study of two-player games with no hidden information and no chance elements. The theory assigns algebraic values to positions in such games and seeks to quantify the algebraic and combinatorial structure of their interactions. Its modern form was introduced thirty years ago, with the publication of the classic Winning Ways for Your Mathematical Plays by Berlekamp, Conway, and Guy, and interest has ra
Table of Contents
- Combinatorial games
- Short games
- The structure of $\mathbb{G}$
- Impartial games
- Misere play
- Loopy games
- Temperature theory
- Transfinite games
- Open problems
- Mathematical prerequisites
- A finite loopfree history
- Bibliography
- Glossary of notation
- Author index
- Index of games
- Index.
