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Game Theory 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. Designed as a textbook for an undergraduate mathematics class and with ample material and limited dependencies between the chapters, Game Theory 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.
Title page 4
Dedication 6
Contents 8
Preface 12
Chapter 1: Combinatorial games 18
Chapter 2: Normal-play games 42
Chapter 3: Impartial games 62
Chapter 4: Hackenbush and partizan games 80
Chapter 5: Zero-sum matrix games 106
Chapter 6: Von Neumann’s Minimax Theorem 128
Chapter 7: General games 150
Chapter 8: Nash equilibrium and applications 178
Chapter 9: Nash’s Equilibrium Theorem 204
Chapter 10: Cooperation 230
Chapter 11: ??-player games 262
Chapter 12: Preferences and society 292
Appendix A: On games and numbers 318
Appendix B: Linear programming 326
Appendix C: Nash equilibrium in high dimensions 340
Game boards 348
Bibliography 352
Index of games 356
Index 358
"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
