GAME THEORY: AN INTRODUCTION

Abstract

Preface. Acknowledgments. Introduction. 1. Matrix 2 person games. 1.1 The Basics. Problems. 1.2 The von Neumann Minimax Theorem. Problems. 1.3 Mixed strategies. 1.3.1 Dominated Strategies. 1.4 Solving 2 x 2 games graphically. Problems. 1.5 Graphical solution of 2 x m and n x 2 games. Problems. 1.6 Best Response Strategies. Problems. 2. Solution Methods for Matrix Games. 2.1 Solution of some special games. 2.1.1 2 x 2 games again. Problems. 2.2 Invertible matrix games. Problems. 2.3 Symmetric games. Problems. 2.4 Matrix games and linear programming. 2.4.1 A direct formulation without transforming. Problems. 2.5 Linear Programming and the Simplex Method (Optional). 2.5.1 The Simplex Method Step by Step. Problems. 2.6 A Game Theory Model of Economic Growth (Optional). Problems. 3. Two Person Nonzero Sum Games. 3.1 The Basics. Problems. 3.2 2 x 2 Bimatrix Games. Problems. 3.3 Interior Mixed Nash Points by Calculus. Problems. 3.3.1 Proof that there is a Nash Equilibrium for Bimatrix Games (Optional). 3.4 Nonlinear Programming Method for Nonzero Sum 2 person Games. Problems. 3.5 Choosing among several Nash Equilibria (Optional). Problems. 4. N Person Nonzero Sum Games with a Continuum of Strategies. 4.1 The Basics. 4.2 Economics applications of Nash equilibria. Problems. 4.2.1 Duels. Problems. 4.3 Auctions (Optional). 4.3.1 Complete Information 208. Problems. 4.3.2 Incomplete Information. 4.3.3 Symmetric Independent Private Value Auctions. Problems. 4.3.4 Symmetric Individual private value auctions again. Problems. 5. Cooperative games. 5.1 Coalitions and Characteristic Functions. Problems. 5.1.1 Finding the least core. Problems. 5.2 The Nucleolus. Problems. 5.3 The Shapley Value. Problems. 5.4 Bargaining. 5.4.1 The Nash model with security point. 5.4.2 Threats. Problems. 6. Evolutionary Stable Strategies and Population games. 6.1 Evolution. Problems. 6.2 Population games. Problems. Appendix A: The essentials of matrix analysis. Appendix B: The essentials of probability. B.0.1 Order Statistics. Appendix C: The Essentials of Maple. Appendix D: The Mathematica commands. Appendix E: Biographies. Appendix F: Solutions to selected Problems. Problem Solutions. References. Index.