## Game Theory and Strategy, Volume 36This book is an introduction to mathematical game theory, which might better be called the mathematical theory of conflict and cooperation. It is applicable whenever two individuals-or companies, or political parties, or nations-confront situations where the outcome for each depends on the behavior of all. What are the best strategies in such situations? If there are chances of cooperation, with whom should you cooperate, and how should you share the proceeds of cooperation? Since its creation by John von Neumann and Oskar Morgenstern in 1944, game theory has shed new light on business, politics, economics, social psychology, philosophy, and evolutionary biology. In this book, its fundamental ideas are developed with mathematics at the level of high school algebra and applied to many of these fields (see the table of contents). Ideas like ``fairness'' are presented via axioms that fair allocations should satisfy; thus the reader is introduced to axiomatic thinking as well as to mathematical modeling of actual situations. |

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User Review - TurtleBoy - LibraryThingGood book! Eminently readable, accessible to even the least experienced of undergraduates (math majors and non-math majors), and full of understandable distillations of realistic game theory ... Read full review

### Contents

The Nature of Games | 3 |

Dominance and Saddle Points | 7 |

Mixed Strategies | 13 |

Jamaican Fishing | 23 |

Guerrillas Police and Missiles | 27 |

Newcombs Problem and Free Will | 32 |

Game Trees | 37 |

Competitive Decision Making | 44 |

The Duopoly Problem | 118 |

APerson Games | 125 |

An Introduction toVPerson Games | 127 |

Strategic Voting | 134 |

VPerson Prisoners Dilemma | 139 |

Prisoners Dilemma and the Football Draft | 145 |

Imputations Domination and Stable Sets | 150 |

Pathan Organization | 161 |

Utility Theory | 49 |

Games Against Nature | 56 |

TwoPerson NonZeroSum Games | 63 |

Nash Equilibria and NonCooperative Solutions | 65 |

The Prisoners Dilemma | 73 |

Trust Suspicion and the FScale | 81 |

Strategic Moves | 85 |

Evolutionarily Stable Strategies | 93 |

The Nash Arbitration Scheme and Cooperative Solutions | 102 |

ManagementLabor Arbitration | 112 |

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### Common terms and phrases

Athena axioms Banzhaf index bargaining set behavior bloc Blues calculate cardinal utilities characteristic function form choice choose coalition structure Colin A B Colin plays column consider cooperation core counter-prudential Divide-the-Dollar dominant strategy equilibrium example Exercises for Chapter expected payoff expected value Figure game theory game tree Gately point give grand coalition guerrillas hawk Hence idea imputation information set Larry line segment lottery Mathematical matrix game method minimax missiles mixed strategy movement diagram Nash equilibrium Neumann nodes non-zero-sum games nucleolus optimal strategy outcome Pareto optimal payoff polygon payoff to Rose players play possible predict preferences Prisoner's Dilemma problem pure strategy rational result Rose and Colin Rose strategy saddle point security level Shapley value Shapley-Shubik index Shapley-Shubik power index situation stable set status quo point subgame Suppose take both boxes take only Box theorem two-person villages voters winning coalitions zero-sum game Zeus