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| Preface for the Second Edition | |
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| Preface for the First Edition | |
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| Acknowledgments | |
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| Introduction | |
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| Matrix Two-Person Games | |
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| The Basics | |
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| Problems | |
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| The von Neumann Mini max Theorem | |
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| Proof of von Neumann's Minimax Theorem (Optional) | |
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| Problems | |
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| Mixed Strategies | |
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| Properties of Optimal Strategies | |
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| Dominated Strategies | |
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| Solving 2 � 2 Games Graphically | |
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| Problems | |
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| Graphical Solution of 2 � m and n � 2 Games | |
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| Problems | |
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| Best Response Strategies | |
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| Problems | |
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| Maple™/Mathematica� | |
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| Bibliographic Notes | |
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| Solution Methods for Matrix Games | |
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| Solution of Some Special Games | |
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| 2 � 2 Games Revisited | |
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| Problems | |
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| Invertible Matrix Games | |
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| Completely Mixed Games | |
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| Problems | |
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| Symmetric Games | |
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| Problems | |
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| Matrix Games and Linear Programming | |
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| Setting Up the Linear Program: Method 1 | |
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| A Direct Formulation Without Transforming: Method 2 | |
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| Problems | |
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| Appendix: Linear Programming and the Simplex Method | |
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| The Simplex Method Step by Step | |
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| Problems | |
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| Review Problems | |
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| Maple/Mathematica | |
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| Invertible Matrices | |
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| Linear Programming: Method 1 | |
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| Linear Programming: Method 2 | |
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| Bibliographic Notes | |
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| Two-Person Nonzero Sum Games | |
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| The Basics | |
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| Problems | |
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| 2 � 2 Bimatrix Games, Best Response, Equality of Payoffs | |
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| Calculation of the Rational Reaction Sets for 2 � 2 Games | |
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| Problems | |
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| Interior Mixed Nash Points by Calculus | |
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| Calculus Method for Interior Nash | |
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| Problems | |
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| Proof that There is a Nash Equilibrium for Bimatrix Games (Optional) | |
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| Nonlinear Programming Method for Nonzero Sum Two-Person Games | |
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| Summary of Methods for Finding Mixed Nash Equilibria | |
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| Problems | |
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| Correlated Equilibria | |
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| LP Problem for a Correlated Equilibrium | |
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| Problems | |
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| Choosing Among Several Nash Equilibria (Optional) | |
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| Problems | |
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| Maple/Mathematica | |
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| Mathematica for Lemke-Howson Algorithm | |
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| Bibliographic Notes | |
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| Games in Extensive Form: Sequential Decision Making | |
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| Introduction to Game Trees-Gambit | |
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| Problems | |
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| Backward Induction and Subgame Perfect Equilibrium | |
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| Problems | |
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| Subgame Perfect Equilibrium | |
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| Examples of Extensive Games Using Gambit | |
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| Problems | |
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| Bibliographic Notes | |
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| N-Person Nonzero Sum Games and Games with a Continuum of Strategies | |
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| The Basics | |
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| Problems | |
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| Economics Applications of Nash Equilibria | |
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| Cournot Duopoly | |
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| A Slight Generalization of Cournot | |
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| Cournot Model with Uncertain Costs | |
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| The Bertrand Model | |
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| The Stackelberg Model | |
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| Entry Deterrence | |
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| Problems | |
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| Duels (Optional) | |
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| Silent Duel on [0, 1] (Optional) | |
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| Problem | |
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| Auctions (Optional) | |
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| Complete Information | |
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| Problems | |
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| Incomplete Information | |
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| Symmetric Independent Private Value Auctions | |
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| Problem | |
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| Bibliographic Notes | |
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| Cooperative Games | |
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| Coalitions and Characteristic Functions | |
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| Problems | |
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| More on the Core and Least Core | |
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| Problems | |
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| The Nucleolus | |
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| An Exact Nucleolus for Three-Player Games | |
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| Problems | |
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| The Shapley Value | |
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| Problems | |
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| Bargaining | |
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| The Nash Model with Security Point | |
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| Threats | |
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| The Kalai-Smorodinsky Bargaining Solution | |
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| Sequential Bargaining | |
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| Problems | |
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| Review Problems | |
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| Maple/Mathematica | |
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| Finding the Nucleolus One Step at a Time | |
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| Mathematica Code for Three-Person Nucleolus | |
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| The Shapley Value with Maple | |
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| Maple and Bargaining | |
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| Bibliographic Notes | |
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| Evolutionary Stable Strategies and Population Games | |
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| Evolution | |
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| Properties of an ESS | |
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| Problems | |
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| Population Games | |
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| Problems | |
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| Bibliographic Notes | |
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| The Essentials of Matrix Analysis | |
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| The Essentials of Probability | |
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| The Essentials of Maple | |
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| The Mathematica Commands | |
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| Biographies | |
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| Problem Solutions | |
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| References | |
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| Index | |