## Matt DeVos and Deborah A. KentThis 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. Designed as a textbook for an undergraduate mathematics class and 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. |

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### Contents

1 | |

Normalplay games | 25 |

Impartial games | 45 |

Hackenbush and partizan games | 63 |

Zerosum matrix games | 89 |

Von Neumanns Minimax Theorem | 111 |

General games | 133 |

Nash equilibrium and applications | 161 |

Preferences and society | 275 |

On games and numbers | 301 |

Linear programming | 309 |

Nash equilibrium in high dimensions | 323 |

Game boards | 331 |

335 | |

339 | |

341 | |

### Common terms and phrases

𝑎 assume axioms 𝐵 best response 𝐶 Chapter choose coalitional game Colin plays combinatorial game combinatorial game theory consider convex hull cooperate Cut-Cake define dominated strategies dyadic number dyadic positions entry envy-free equation equivalent expected payoff 𝑓 Figure fixed point property function game 𝐴 game theory game tree gives Grim Trigger guarantee Hackenbush Hackenbush position impartial game imputation induction 𝑘 label Lemma linear Louise 𝑚 mixed strategy 𝑛 Nash equilibrium Nash flow Nash’s negotiation set Neumann solution node nonnegative normal-play games outcome 𝑝 partizan games payoff matrix payoff polygon Pick-Up-Bricks plays row position of type proof prove pure Nash pure strategy 𝑞 𝑅 result Richard Rose and Colin Rose plays Rose-Colin Rose's Rose’s row 𝑖 𝑆 second player Shapley Value solution point strategy for Rose strategy q strategy space Suppose tion 𝑣 valuation scheme vector voter 𝑤 winning 𝑋 𝑌 zero-sum matrix game 𝛼 𝛽 𝛾