Combinatorial Game Theory

Aaron N. Siegel

• Publisher: American Mathematical Society
• Year: 2013
• Topic: Mathematics
• eBook ISBN:
  9781470409449
• Subtopic: Mathematics General
• Index: Mathematics

It 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 rapidly increased in recent decades. This book is a comprehensive and up-to-date introduction to the subject, tracing its development from first principles and examples through many of its most recent advances. Roughly half the book is devoted to a rigorous treatment of the classical theory; the remaining material is an in-depth presentation of topics that appear for the first time in textbook form, including the theory of misère quotients and Berlekamp's generalized temperature theory. Packed with hundreds of examples and exercises and meticulously cross-referenced, Combinatorial Game Theory will appeal equally to students, instructors, and research professionals. More than forty open problems and conjectures are mentioned in the text, highlighting the many mysteries that still remain in this young and exciting field. Aaron Siegel holds a Ph.D. in mathematics from the University of California, Berkeley and has held positions at the Mathematical Sciences Research Institute and the Institute for Advanced Study. He was a partner at Berkeley Quantitative, a technology-driven hedge fund, and is presently employed by Twitter, Inc.

Table of contents

• Front Cover
• Contents
• Preface
• Chapter I Combinatorial Games
• Chapter II Short Games
• Chapter III The Structure of G
• Chapter IV Impartial Games
• Chapter V Mis`ere Play
• Chapter VI Loopy Games
• Chapter VII Temperature Theory
• Chapter VIII Transfinite Games
• Appendix A Open Problems
• Appendix B Mathematical Prerequisites
• Appendix C A Finite Loopfree History
• Bibliography
• Glossary of Notation
• Author Index
• Index of Games
• Index
• Back Cover