Game Theory
An Introduction
(Sprache: Englisch)
This book confirms the role of mathematics in making logical and advantageous decisions and uses modern software applications to create, analyze, and implement effective decision-making models. This Second Edition of the bestselling book provides a balanced...
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Produktinformationen zu „Game Theory “
This book confirms the role of mathematics in making logical and advantageous decisions and uses modern software applications to create, analyze, and implement effective decision-making models. This Second Edition of the bestselling book provides a balanced treatment of the subject that is both conceptual and hands-on.
Klappentext zu „Game Theory “
An exciting new edition of the popular introduction to game theory and its applicationsThe thoroughly expanded Second Edition presents a unique, hands-on approach to game theory. While most books on the subject are too abstract or too basic for mathematicians, Game Theory: An Introduction, Second Edition offers a blend of theory and applications, allowing readers to use theory and software to create and analyze real-world decision-making models.
With a rigorous, yet accessible, treatment of mathematics, the book focuses on results that can be used to determine optimal game strategies. Game Theory: An Introduction, Second Edition demonstrates how to use modern software, such as Maple(TM), Mathematica(r), and Gambit, to create, analyze, and implement effective decision-making models. Coverage includes the main aspects of game theory including the fundamentals of two-person zero-sum games, cooperative games, and population games as well as a large number of examples from various fields, such as economics, transportation, warfare, asset distribution, political science, and biology. The Second Edition features:
* A new chapter on extensive games, which greatly expands the implementation of available models
* New sections on correlated equilibria and exact formulas for three-player cooperative games
* Many updated topics including threats in bargaining games and evolutionary stable strategies
* Solutions and methods used to solve all odd-numbered problems
* A companion website containing the related Maple and Mathematica data sets and code
A trusted and proven guide for students of mathematics and economics, Game Theory: An Introduction, Second Edition is also an excellent resource for researchers and practitioners in economics, finance, engineering, operations research, statistics, and computer science.
Inhaltsverzeichnis zu „Game Theory “
Preface for the Second Edition xiPreface for the First Edition xv
Acknowledgments xvii
Introduction 1
1 Matrix Two-Person Games 5
1.1 The Basics, 5
Problems, 16
1.2 The von Neumann Minimax Theorem, 18
1.2.1 Proof of von Neumann's Minimax Theorem (Optional), 21
Problems, 24
1.3 Mixed Strategies, 25
1.3.1 Properties of Optimal Strategies, 35
1.3.2 Dominated Strategies, 38
1.4 Solving 2 × 2 Games Graphically, 41
Problems, 43
1.5 Graphical Solution of 2 × m and n × 2 Games, 44
Problems, 50
1.6 Best Response Strategies, 53
Problems, 57
1.6.1 MapleTM/Mathematica R , 58
Bibliographic Notes, 59
2 Solution Methods for Matrix Games 60
2.1 Solution of Some Special Games, 60
2.1.1 2 × 2 Games Revisited, 60
Problems, 64
2.2 Invertible Matrix Games, 65
2.2.1 Completely Mixed Games,68
Problems, 74
2.3 Symmetric Games, 76
Problems, 81
2.4 Matrix Games and Linear Programming, 82
2.4.1 Setting Up the Linear Program: Method 1, 83
2.4.2 A Direct Formulation Without Transforming: Method 2, 89
Problems, 94
2.5 Appendix: Linear Programming and the Simplex Method, 98
2.5.1 The Simplex Method Step by Step, 101
Problems, 108
2.6 Review Problems, 108
2.7 Maple/Mathematica, 109
2.7.1 Invertible Matrices, 109
2.7.2 Linear Programming: Method 1, 110
2.7.3 Linear Programming: Method 2, 111
Bibliographic Notes, 113
3 Two-Person Nonzero Sum Games 115
3.1 The Basics, 115
Problems, 123
3.2 2 × 2 Bimatrix Games, Best Response, Equality of Payoffs, 125
3.2.1 Calculation of the Rational Reaction Sets for 2 × 2 Games, 125
Problems, 132
3.3 Interior Mixed Nash Points by
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Calculus, 135
3.3.1 Calculus Method for Interior Nash, 135
Problems, 143
3.3.2 Proof that There is a Nash Equilibrium for Bimatrix Games (Optional), 146
3.4 Nonlinear Programming Method for Nonzero Sum Two-Person Games, 148
3.4.1 Summary of Methods for Finding Mixed Nash Equilibria, 156
Problems, 158
3.5 Correlated Equilibria, 159
3.5.1 LP Problem for a Correlated Equilibrium, 165
Problems, 166
3.6 Choosing Among Several Nash Equilibria (Optional), 167
Problems, 172
3.6.1 Maple/Mathematica, 173
3.6.2 Mathematica for Lemke-Howson Algorithm, 173
Bibliographic Notes, 175
4 Games in Extensive Form: Sequential Decision Making 176
4.1 Introduction to Game Trees--Gambit, 176
Problems, 189
4.2 Backward Induction and Subgame Perfect Equilibrium, 190
Problems, 193
4.2.1 Subgame Perfect Equilibrium, 194
4.2.2 Examples of Extensive Games Using Gambit, 200
Problems, 209
Bibliographic Notes, 212
5 n-Person Nonzero Sum Games and Games with a Continuum of Strategies 213
5.1 The Basics, 213
Problems, 235
5.2 Economics Applications of Nash Equilibria, 242
5.2.1 Cournot Duopoly, 243
5.2.2 A Slight Generalization of Cournot, 245
5.2.3 Cournot Model with Uncertain Costs, 247
5.2.4 The Bertrand Model, 250
5.2.5 The Stackelberg Model, 252
5.2.6 Entry Deterrence, 254
Problems, 256
5.3 Duels (Optional), 259
5.3.1 Silent Duel on [0,1] (
3.3.1 Calculus Method for Interior Nash, 135
Problems, 143
3.3.2 Proof that There is a Nash Equilibrium for Bimatrix Games (Optional), 146
3.4 Nonlinear Programming Method for Nonzero Sum Two-Person Games, 148
3.4.1 Summary of Methods for Finding Mixed Nash Equilibria, 156
Problems, 158
3.5 Correlated Equilibria, 159
3.5.1 LP Problem for a Correlated Equilibrium, 165
Problems, 166
3.6 Choosing Among Several Nash Equilibria (Optional), 167
Problems, 172
3.6.1 Maple/Mathematica, 173
3.6.2 Mathematica for Lemke-Howson Algorithm, 173
Bibliographic Notes, 175
4 Games in Extensive Form: Sequential Decision Making 176
4.1 Introduction to Game Trees--Gambit, 176
Problems, 189
4.2 Backward Induction and Subgame Perfect Equilibrium, 190
Problems, 193
4.2.1 Subgame Perfect Equilibrium, 194
4.2.2 Examples of Extensive Games Using Gambit, 200
Problems, 209
Bibliographic Notes, 212
5 n-Person Nonzero Sum Games and Games with a Continuum of Strategies 213
5.1 The Basics, 213
Problems, 235
5.2 Economics Applications of Nash Equilibria, 242
5.2.1 Cournot Duopoly, 243
5.2.2 A Slight Generalization of Cournot, 245
5.2.3 Cournot Model with Uncertain Costs, 247
5.2.4 The Bertrand Model, 250
5.2.5 The Stackelberg Model, 252
5.2.6 Entry Deterrence, 254
Problems, 256
5.3 Duels (Optional), 259
5.3.1 Silent Duel on [0,1] (
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Autoren-Porträt von E. N. Barron
E. N. BARRON, PhD, is Professor of Mathematics and Statistics in the Department of Mathematics and Statistics at Loyola University Chicago and the author of more than sixty journal articles on optimal control, differential games, nonlinear partial differential equations, and mathematical finance.
Bibliographische Angaben
- Autor: E. N. Barron
- 2013, 2. Aufl., 574 Seiten, mit Abbildungen, Maße: 18,3 x 26 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 1118216938
- ISBN-13: 9781118216934
- Erscheinungsdatum: 12.04.2013
Sprache:
Englisch
Pressezitat
"I highly recommend the superb and very practical textbook Game Theory: An Introduction, Second Edition by E.N. Barron, Ph.D., along with its very useful learning companion book Solutions Manual to Accompany Game Theory: An Introduction, Second Edition also by E.N. Barron, Ph.D., to any academic instructors of game theory, especially those who teach a wide range of students from many different disciplines. This textbook provides the foundational aspects of game theory in an approachable and hands on format that will appeal to both professors and students alike." ( B log Business World , 21 September 2013)Kommentar zu "Game Theory"
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