Barron Game Theory

An Introduction
1. Auflage 2011
ISBN: 978-1-118-03065-3
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 440 Seiten, E-Book

A fundamental introduction to modern game theory from amathematical viewpoint
Game theory arises in almost every fact of human and inhumaninteraction since oftentimes during these communications objectivesare opposed or cooperation is viewed as an option. From economicsand finance to biology and computer science, researchers andpractitioners are often put in complex decision-making scenarios,whether they are interacting with each other or working withevolving technology and artificial intelligence. Acknowledging therole of mathematics in making logical and advantageous decisions,Game Theory: An Introduction uses modern software applications tocreate, analyze, and implement effective decision-makingmodels.
While most books on modern game theory are either too abstractor too applied, this book provides a balanced treatment of thesubject that is both conceptual and hands-on. Game Theoryintroduces readers to the basic theories behind games and presentsreal-world examples from various fields of study such as economics,political science, military science, finance, biological science aswell as general game playing. A unique feature of this book is theuse of Maple to find the values and strategies of games, and inaddition, it aids in the implementation of algorithms for thesolution or visualization of game concepts. Maple is also utilizedto facilitate a visual learning environment of game theory and actsas the primary tool for the calculation of complex non-cooperativeand cooperative games.
Important game theory topics are presented within the followingfive main areas of coverage:
* Two-person zero sum matrix games
* Nonzero sum games and the reduction to nonlinear programming
* Cooperative games, including discussion of both the Nucleolusconcept and the Shapley value
* Bargaining, including threat strategies
* Evolutionary stable strategies and population games
Although some mathematical competence is assumed, appendices areprovided to act as a refresher of the basic concepts of linearalgebra, probability, and statistics. Exercises are included at theend of each section along with algorithms for the solution of thegames to help readers master the presented information. Also,explicit Maple and Mathematica® commands are included in thebook and are available as worksheets via the book's related Website. The use of this software allows readers to solve many moreadvanced and interesting games without spending time on the theoryof linear and nonlinear programming or performing other complexcalculations.
With extensive examples illustrating game theory's wide range ofrelevance, this classroom-tested book is ideal for game theorycourses in mathematics, engineering, operations research, computerscience, and economics at the upper-undergraduate level. It is alsoan ideal companion for anyone who is interested in the applicationsof game theory.

Autoren/Hrsg.

Barron, E. N.

Inhaltsverzeichnis

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 2games.
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 personGames.
Problems.
3.5 Choosing among several Nash Equilibria (Optional).
Problems.
4. N Person Nonzero Sum Games with a Continuum ofStrategies.
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 Populationgames.
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.

Über Autor(innen)

E. N. Barron, PhD, is Professor of Mathematical Sciences in the Department of Mathematics and Statistics at Loyola University Chicago. He is the author of over fifty research journal articles, and his teaching experience includes optimal control, stochastic processes, differential games, analysis, operations research, game theory, and financial mathematics, among others.