Game Theory: An Introduction
While most books on game theory are either too applied or too abstract, this book finds a nice balance between the two, and in addition, it does not focus on linear programming. This is the first book to utilize computer software (MapleTM and Mathematica®) to do the types of linear programming involved in game theory since Maple can solve linear and nonlinear programs very quickly and easily. This allows students and readers to solve many more advanced and interesting games without spending time on the theory of linear programming. The focus of the book is not on proofs, but some proofs are provided for important results.
1. Matrix 2 person games.
1.1 The Basics.
1.2 The von Neumann Minimax Theorem.
1.3 Mixed strategies.
1.3.1 Dominated Strategies.
1.4 Solving 2 x 2 games graphically.
1.5 Graphical solution of 2 x m and n x 2 games.
1.6 Best Response Strategies.
2. Solution Methods for Matrix Games.
2.1 Solution of some special games.
2.2 Invertible matrix games.
2.3 Symmetric games.
2.4 Matrix games and linear programming.
2.4.1 A direct formulation without transforming.
2.5 Linear Programming and the Simplex Method (Optional).
2.6 A Game Theory Model of Economic Growth (Optional).
3. Two Person Nonzero Sum Games.
3.1 The Basics.
3.2 2 x 2 Bimatrix Games.
3.3 Interior Mixed Nash Points by Calculus.
3.4 Nonlinear Programming Method for Nonzero Sum 2 person Games.
3.5 Choosing among several Nash Equilibria (Optional).
4. N Person Nonzero Sum Games with a Continuum of Strategies.
4.1 The Basics.
4.2 Economics applications of Nash equilibria.
4.3 Auctions (Optional).
5. Cooperative games.
5.1 Coalitions and Characteristic Functions.
5.2 The Nucleolus.
5.3 The Shapley Value.
6. Evolutionary Stable Strategies and Population games.
6.2 Population games.
Appendix A: The essentials of matrix analysis.
Appendix B: The essentials of probability.
Appendix C: The Essentials of Maple.
Appendix D: The Mathematica commands.
Appendix E: Biographies.
Appendix F: Solutions to selected Problems.