Table of Contents

Foreword ix 1 Matrix Two-Person Games 1

1.1 The Basics, 1

1.2 The von Neumann Minimax Theorem, 6

1.4 Solving 2 x 2 Games Graphically, 9

1.5 Graphical Solution of 2 x m and n x 2 Games, 12

1.6 Best Response Strategies, 22

2 Solution Methods for Matrix Games 26

2.1 Solution of Some Special Games, 26

2.2 Invertible Matrix Games, 29

2.3 Symmetric Games, 37

2.4 Matrix Games and Linear Programming, 41

2.5 Appendix: Linear Programming and the Simplex Method, 60

2.6 Review Problems, 61

3 Two-Person Nonzero Sum Games 65

3.1 The Basics, 65

3.2 2 x 2 Bimatrix Games, Best Response, Equality of Payoffs, 69

3.3 Interior Mixed Nash Points by Calculus, 80

3.4 Nonlinear Programming Method for Nonzero Sum Two-Person Games, 90

3.5 Correlated Equilibria, 94

3.6 Choosing Among Several Nash Equilibria, 98

4 Games in Extensive Form: Sequential Decision Making 101

4.1 Introduction to Game Trees-Gambit, 101

4.2 Backward Induction and Subgame Perfect Equilibrium, 106

4.2.2 Examples of Extensive Games Using Gambit, 108

5 n-Person Nonzero Sum Games and Games with a Continuum of Strategies 129

5.1 The Basics, 129

5.2 Economics Applications of Nash Equilibria, 152

5.3 Duels, 163

5.4 Auctions, 163

5.4.1 Complete Information, 163

5.4.2 Incomplete Information, 165

6 Cooperative Games 166

6.1 Coalitions and Characteristic Functions, 166

6.1.1 More on the Core and Least Core, 174

6.2 The Nucleolus, 178

6.3 The Shapley Value, 186

6.4 Bargaining, 204

Review Problems, 213

7 Evolutionary Stable Strategies and Population Games 215

7.1 Evolution, 215

7.2 Population Games, 219

Appendix: The Main Definitions and Theorems 231

A Matrix Two-Person Games 233

B Solution Methods for Matrix Games 237

C Two-Person Nonzero Sum Games 240

D Games in Extensive Form: Sequential Decision Making 245

E n-Person Nonzero Sum Games and Games with a Continuum of Strategies 246

F Cooperative Games 248

G Evolutionary Stable Strategies and Population Games 252

Index 255

About the Author

E. N. Barron is the author of Solutions Manual to Accompany Game Theory: An Introduction, 2nd Edition, published by Wiley.