Game Theory

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.

Game Theory: A Playful Introduction is exactly as the title claims: an interactive introduction to the subject. It is a well-written text which starts with a thorough analysis of combinatorial game theory before smoothly transitioning to classical game theory...Not only is the text readable, but there are also an adequate number of exercises at the end of each chapter. These exercises are structured as a scaffold beginning with a check of basic skills and building up to challenging proofs...Overall, this text is a well-structured, well-written introduction to game theory." — Brittany Shelton, Mathematical Reviews"The topics covered here are chosen for a broad and versatile look at the subject, the writing style is clear and enjoyable, examples are plentiful, and there is a good selection of exercises, both computational and proof-oriented...In addition to clear and engaging writing, and a good selection of exercises, this book also boasts an excellent bibliography...I have no hesitation whatsoever recommending it as a text for an introductory undergraduate course." — Mark Hunacek, MAA Reviews

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