E. N. Barron

Game Theory (eBook, ePUB)

An Introduction

• Format: ePub

Produktbeschreibung

An exciting new edition of the popular introduction to game theory and its applications The 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®, 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.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 574
• Erscheinungstermin: 9. April 2013
• Englisch
• ISBN-13: 9781118533895
• Artikelnr.: 38402531

Autorenporträt

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.

Inhaltsangabe

Preface for the Second Edition xi Preface 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 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] (Optional)
262 Problem
266 5.4 Auctions (Optional)
266 5.4.1 Complete Information
271 Problems
272 5.4.2 Incomplete Information
272 5.4.3 Symmetric Independent Private Value Auctions
275 Problem
286 Bibliographic Notes
287 6 Cooperative Games 288 6.1 Coalitions and Characteristic Functions
288 Problems
307 6.1.1 More on the Core and Least Core
310 Problems
317 6.2 The Nucleolus
319 6.2.1 An Exact Nucleolus for Three-Player Games
327 Problems
333 6.3 The Shapley Value
335 Problems
347 6.4 Bargaining
352 6.4.1 The Nash Model with Security Point
358 6.4.2 Threats
365 6.4.3 The Kalai-Smorodinsky Bargaining Solution
377 6.4.4 Sequential Bargaining
379 Problems
384 Review Problems
386 6.5 Maple/Mathematica
386 6.5.1 Finding the Nucleolus One Step at a Time
386 6.5.2 Mathematica Code for Three-Person Nucleolus
391 6.5.3 The Shapley Value with Maple
393 6.5.4 Maple and Bargaining
393 Bibliographic Notes
394 7 Evolutionary Stable Strategies and Population Games 395 7.1 Evolution
395 7.1.1 Properties of an ESS
402 Problems
408 7.2 Population Games
409 Problems
428 Bibliographic Notes
430 Appendix A: The Essentials of Matrix Analysis 432 Appendix B: The Essentials of Probability 436 Appendix C: The Essentials of Maple 442 Appendix D: The Mathematica Commands 448 Appendix E: Biographies 463 Problem Solutions 465 References 549 Index 551

Rezensionen

"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." (Blog Business World, 21 September 2013)