Essentials Of Game Theory / Edition 1

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Overview

Game 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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Product Details

Table of Contents

Credits and Acknowledgments xiii

Preface xv

1 Games in Normal Form 1

1.1 Example: The TCP User's Game 2

1.2 Definition of Games in Normal Form 3

1.3 More Examples of Normal-Form Games 4

1.3.1 Prisoner's Dilemma 4

1.3.2 Common-payoff Games 4

1.3.3 Zero-sum Games 5

1.3.4 Battle of the Sexes 7

1.4 Strategies in Normal-form Games 7

2 Analyzing Games: From Optimality to Equilibrium 9

2.1 Pareto optimality 9

2.2 Defining Best Response and Nash Equilibrium 10

2.3 Finding Nash Equilibria 11

3 Further Solution Concepts for Normal-Form Games 15

3.1 Maxmin and Minmax Strategies 15

3.2 Minimax Regret 18

3.3 Removal of Dominated Strategies 20

3.4 Rationalizability 23

3.5 Correlated Equilibrium 24

3.6 Trembling-Hand Perfect Equilibrium 26

3.7 $$-Nash Equilibrium 27

3.8 Evolutionarily Stable Strategies 28

4 Games With Sequential Actions: The Perfect-information Extensive Form 31

4.1 Definition 31

4.2 Strategies and Equilibria 32

4.3 Subgame-Perfect Equilibrium 35

4.4 Backward Induction 38

5 Generalizing the Extensive Form: Imperfect-Information Games 41

5.1 Definition 41

5.2 Strategies and Equilibria 42

5.3 Sequential Equilibrium 45

6 Repeated and Stochastic Games 49

6.1 Finitely Repeated Games 49

6.2 Infinitely Repeated Games 50

6.3 Stochastic Games 53

6.3.1 Definition 53

6.3.2 Strategies and Equilibria 54

7 Uncertainty About Payoffs: Bayesian Games 57

7.1 Definition 59

7.1.1 Information Sets 59

7.1.2 Extensive Form with Chance Moves 60

7.1.3 Epistemic Types 6$$

7.2 Strategies and Equilibria 6$$

7.3 Computing Equilibria 6$$

7.4 Ex-post Equilibria 6$$

8 Coalitional Game Theory 6$$

8.1Coalitional Games with Transferable Utility 6$$

8.2 Classes of Coalitional Games 7$$

8.3 Analyzing Coalitional Games 7$$

8.3.1 The Shapley Value 7$$

8.3.2 The Core 7$$

History and References 7$$

References $$

Index $$

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