This book offers a gentle introduction to the mathematics of both sides of game theory: combinatorial and classical. The combination allows for a dynamic and rich tour of the subject united by a common theme of strategic reasoning.

The first four chapters develop combinatorial game theory, beginning with an introduction to game trees and mathematical induction, then investigating the games of Nim and Hackenbush. The analysis of these games concludes with the cornerstones of the Sprague-Grundy Theorem and the Simplicity Principle.

The last eight chapters of the book offer a scenic journey through the mathematical highlights of classical game theory. This contains a thorough treatment of zero-sum games and the von Neumann Minimax Theorem, as well as a student-friendly development and proof of the Nash Equilibrium Theorem. The Folk Theorem, Arrow's voting paradox, evolutionary biology, cake cutting, and other engaging auxiliary topics also appear.

The book is designed as a textbook for an undergraduate mathematics class. With ample material and limited dependencies between the chapters, the book is adaptable to a variety of situations and a range of audiences. Instructors, students, and independent readers alike will appreciate the flexibility in content choices as well as the generous sets of exercises at various levels.

Matt DeVos,  Simon Fraser University, Burnaby, BC, Canada
Deborah A. Kent, Drake University, Des Moines, IA

Chapter 1. Combinatorial games
Chapter 2. Normal-play games
Chapter 3. Impartial games
Chapter 4. Hackenbush and partizan games
Chapter 5. Zero-sum matrix games
Chapter 6. Von Neumann’s Minimax Theorem
Chapter 7. General games
Chapter 8. Nash equilibrium and applications
Chapter 9. Nash’s Equilibrium Theorem
Chapter 10. Cooperation
Chapter 11. -player games
Chapter 12. Preferences and society
Appendix A. On games and numbers
Appendix B. Linear programming
Appendix C. Nash equilibrium in high dimensions