Solutions Manual to Accompany Game Theory
An Introduction
2. Edition May 2013
266 Pages, Softcover
Wiley & Sons Ltd
ISBN:
978-1-118-27428-6
John Wiley & Sons
An invaluable study aid for students of game theory
Solutions Manual to accompany Game Theory: An Introduction, 2nd Edition provides complete explanations and fully worked solutions for the problems posed in the text. Although designed as a supplement to Game Theory, this solutions guide is versatile enough to act as an independent review of key topics, regardless of which textbook you are using. Each solution includes the original question as well as all given data, and clear, concise language describes the approach and reasoning that yields the correct solution.
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 × 2 Games Graphically, 9
1.5 Graphical Solution of 2 × m and n × 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 × 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
1 Matrix Two-Person Games 1
1.1 The Basics, 1
1.2 The von Neumann Minimax Theorem, 6
1.4 Solving 2 × 2 Games Graphically, 9
1.5 Graphical Solution of 2 × m and n × 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 × 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
E. N. Barron is the author of Solutions Manual to Accompany Game Theory: An Introduction, 2nd Edition, published by Wiley.
