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Game Theory: An Introduction, 2nd Edition

Book Description

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™, 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.

Note: The ebook version does not provide access to the companion files.

Table of Contents

  1. Cover
  2. Wiley Series in Operations Research and Management Science
  3. Title Page
  4. Copyright
  5. Dedication
  6. Preface for the Second Edition
  7. Preface for the First Edition
  8. Acknowledgments
  9. Introduction
  10. Chapter One: Matrix Two-Person Games
    1. 1.1 The Basics
    2. 1.2 The von Neumann Minimax Theorem
    3. 1.3 Mixed Strategies
    4. 1.4 Solving 2 × 2 Games Graphically
    5. 1.5 Graphical Solution of 2 × m and n × 2 Games
    6. 1.6 Best Response Strategies
    7. Bibliographic Notes
  11. Chapter Two: Solution Methods for Matrix Games
    1. 2.1 Solution of Some Special Games
    2. 2.2 Invertible Matrix Games
    3. 2.3 Symmetric Games
    4. 2.4 Matrix Games and Linear Programming
    5. 2.5 Appendix: Linear Programming and the Simplex Method
    6. 2.6 Review Problems
    7. 2.7 Maple/Mathematica
    8. Bibliographic Notes
  12. Chapter Three: Two-Person Nonzero Sum Games
    1. 3.1 The Basics
    2. 3.2 2 × 2 Bimatrix Games, Best Response, Equality of Payoffs
    3. 3.3 Interior Mixed Nash Points by Calculus
    4. 3.4 Nonlinear Programming Method for Nonzero Sum Two-Person Games
    5. 3.5 Correlated Equilibria
    6. 3.6 Choosing Among Several Nash Equilibria (Optional)
    7. Bibliographic Notes
  13. Chapter Four: Games in Extensive Form: Sequential Decision Making
    1. 4.1 Introduction to Game Trees—Gambit
    2. 4.2 Backward Induction and Subgame Perfect Equilibrium
    3. Bibliographic Notes
  14. Chapter Five: N-Person Nonzero Sum Games and Games with a Continuum of Strategies
    1. 5.1 The Basics
    2. 5.2 Economics Applications of Nash Equilibria
    3. 5.3 Duels (Optional)
    4. 5.4 Auctions (Optional)
    5. Bibliographic Notes
  15. Chapter Six: Cooperative Games
    1. 6.1 Coalitions and Characteristic Functions
    2. 6.2 The Nucleolus
    3. 6.3 The Shapley Value
    4. 6.4 Bargaining
    5. 6.5 Maple/Mathematica
    6. Bibliographic Notes
  16. Chapter Seven: Evolutionary Stable Strategies and Population Games
    1. 7.1 Evolution
    2. 7.2 Population Games
    3. Bibliographic Notes
  17. Appendix A: The Essentials of Matrix Analysis
  18. Appendix B: The Essentials of Probability
    1. B.1 Discrete Random Variables
    2. B.2 Continuous Distributions
    3. B.3 Order Statistics
  19. Appendix C: The Essentials of Maple
    1. C.1 Features
    2. C.2 Functions
    3. C.3 Some Commands Used in This Book
  20. Appendix D: The Mathematica Commands
    1. D.1 The Upper and Lower Values of a Game
    2. D.2 The Value of an Invertible Matrix Game with Mixed Strategies
    3. D.3 Solving Matrix Games by Linear Programming
    4. D.4 Interior Nash Points
    5. D.5 Lemke–Howson Algorithm for Nash Equilibrium
    6. D.6 Is the Core Empty?
    7. D.7 Find and Plot the Least Core
    8. D.8 Nucleolus and Shapley Value Procedure
    9. D.9 Plotting the Payoff Pairs
    10. D.10 Bargaining Solutions
    11. D.11 Mathematica for Replicator Dynamics
  21. Appendix E: Biographies
    1. E.1 John von Neumann
    2. E.2 John Forbes Nash
  22. Problem Solutions
    1. Solutions for Chapter 1
    2. Solutions for Chapter 2
    3. Solutions for Chapter 3
    4. Solutions for Chapter 4
    5. Solutions for Chapter 5
    6. Solutions for Chapter 6
    7. Solutions for Chapter 7
  23. References
  24. Index