1. Edition - February 2008 102.- Euro 2008. 440 Pages, Hardcover ISBN-10: 0-470-17132-4 ISBN-13: 978-0-470-17132-5 - John Wiley & Sons
Short description This is the first book to utilize computer software (Maple(tm) and Mathematica(r)) to do the types of linear programming involved in game theory, allowing 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. Algorithms for solutions to the games are presented in detail, and interesting applications are used to illustrate the theory.
From the contents 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.
