Game Theory: An Introduction

Game Theory: An Introduction

Hardback Wiley Series in Operations Research and Management Science

By (author) E. N. Barron

$85.74
List price $114.81
You save $29.07 25% off

Free delivery worldwide
Available
Dispatched in 4 business days
When will my order arrive?

  • Publisher: John Wiley & Sons Inc
  • Format: Hardback | 574 pages
  • Dimensions: 185mm x 251mm x 36mm | 1,134g
  • Publication date: 1 June 2013
  • Publication City/Country: New York
  • ISBN 10: 1118216938
  • ISBN 13: 9781118216934
  • Edition: 2, Revised
  • Edition statement: 2nd Revised edition
  • Illustrations note: Illustrations (black and white)
  • Sales rank: 645,686

Product description

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. The book introduces the basic theories behind games and presents real-world examples from various fields of study such as economics, political science, military science, finance, biological science as well as general game playing. In addition to two new chapters on Games in Extensive Form: Sequential Decision Making and Repeated, Recursive, and Stochastic Games, and many new topics have been added and revised.

Other people who viewed this bought:

Showing items 1 to 10 of 10

Other books in this category

Showing items 1 to 11 of 11
Categories:

Author information

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.

Review quote

"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)

Back cover copy

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 modelsNew sections on correlated equilibria and exact formulas for three-player cooperative gamesMany updated topics including threats in bargaining games and evolutionary stable strategiesSolutions and methods used to solve all odd-numbered problemsA companion website containing the related Maple and Mathematica data sets and codeA 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.

Table of contents

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