## Essentials of Game Theory: A Concise, Multidisciplinary IntroductionGame theory is the mathematical study of interaction among independent, self-interested agents. The audience for game theory has grown dramatically in recent years, and now spans disciplines as diverse as political science, biology, psychology, economics, linguistics, sociology, and computer science, among others. What has been missing is a relatively short introduction to the field covering the common basis that anyone with a professional interest in game theory is likely to require. Such a text would minimize notation, ruthlessly focus on essentials, and yet not sacrifice rigor. This Synthesis Lecture aims to fill this gap by providing a concise and accessible introduction to the field. It covers the main classes of games, their representations, and the main concepts used to analyze them. Table of Contents: Games in Normal Form / Analyzing Games: From Optimality to Equilibrium / Further Solution Concepts for Normal-Form Games / Games with Sequential Actions: The Perfect-information Extensive Form / Generalizing the Extensive Form: Imperfect-Information Games / Repeated and Stochastic Games / Uncertainty about Payoffs: Bayesian Games / Coalitional Game Theory / History and References / Index |

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#### LibraryThing Review

User Review - HadriantheBlind - LibraryThingGood grounding in the basics of game theory. Can be a bit rough if you have absolutely no compsci/etc. background, but very interesting nonetheless. Read full review

### Contents

Games in Normal Form | 1 |

THE TCP USERS GAME | 2 |

12 DEFINITION OF GAMES IN NORMAL FORM | 3 |

132 Commonpayoff Games | 4 |

133 Zerosum Games | 5 |

134 Battle of the Sexes | 6 |

Analyzing Games From Optimality To Equilibrium | 9 |

22 DEFINING BEST RESPONSE AND NASH EQUILIBRIUM | 10 |

52 STRATEGIES AND EQUILIBRIA | 42 |

53 SEQUENTIAL EQUILIBRIUM | 45 |

Repeated and Stochastic Games | 49 |

62 INFINITELY REPEATED GAMES | 50 |

63 STOCHASTIC GAMES | 53 |

632 Strategies and Equilibria | 54 |

Uncertainty About Payoffs Bayesian Games | 57 |

71 DEFINITION | 59 |

23 FINDING NASH EQUILIBRIA | 11 |

Further Solution Concepts for NormalForm Games | 15 |

32 MINIMAX REGRET | 18 |

33 REMOVAL OF DOMINATED STRATEGIES | 20 |

34 RATIONALIZABILITY | 23 |

35 CORRELATED EQUILIBRIUM | 24 |

36 TREMBLINGHAND PERFECT EQUILIBRIUM | 26 |

37 ϵNASH EQUILIBRIUM | 27 |

38 EVOLUTIONARILY STABLE STRATEGIES | 28 |

Games With Sequential Actions The PerfectInformation Extensive Form | 31 |

42 STRATEGIES AND EQUILIBRIA | 32 |

43 SUBGAMEPERFECT EQUILIBRIUM | 35 |

44 BACKWARD INDUCTION | 38 |

Generalizing the Extensive Form ImperfectInformation Games | 41 |

712 Extensive form with Chance Moves | 60 |

713 Epistemic Types | 61 |

73 COMPUTING EQUILIBRIA | 64 |

74 EXPOST EQUILIBRIA | 67 |

Coalitional Game Theory | 69 |

82 CLASSES OF COALITIONAL GAMES | 70 |

83 ANALYZING COALITIONAL GAMES | 72 |

831 The Shapley Value | 73 |

832 The Core | 75 |

History and References | 79 |

83 | |

85 | |

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### Common terms and phrases

action proﬁle agent i’s algorithm backward induction Bayesian game behavioral strategies best response Chapter choice nodes choose coalitional game theory column player common-payoff games core correlated equilibrium deﬁned Deﬁnition evolutionarily stable strategy example expected payoff expected utility extensive form ﬁnal ﬁnd ﬁrst game from Figure game G game in extensive game in Figure game theory games of perfect given grand coalition induced normal form inﬁnitely repeated games information set Intuitively Matching Pennies maxmin strategy maxmin value minmax strategy minmax value mixed strategies mixed-strategy proﬁle n-player Nash equilibrium normal-form game notion outcome payoff proﬁle payoff vector perfect recall perfect-information games player 1’s Prisoner’s Dilemma game probability distribution pure strategy rationalizable strategies reduced game repeated games row player Shapley value solution concepts stage game stochastic game strategy for player strategy proﬁle strategy space subgame subgame-perfect equilibrium superadditive Theorem ui(si utility function weakly zero-sum games