Combinatorial Game Theory

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.