Game Theory (eBook)

An Introduction

E. N. Barron (Autor)

eBook Download: PDF

2011 | 1. Auflage
440 Seiten
John Wiley & Sons (Verlag)
978-1-118-03065-3 (ISBN)

Infos

A fundamental introduction to modern game theory from a
mathematical viewpoint

Game theory arises in almost every fact of human and inhuman
interaction since oftentimes during these communications objectives
are opposed or cooperation is viewed as an option. From economics
and finance to biology and computer science, researchers and
practitioners are often put in complex decision-making scenarios,
whether they are interacting with each other or working with
evolving technology and artificial intelligence. Acknowledging the
role of mathematics in making logical and advantageous decisions,
Game Theory: An Introduction uses modern software applications to
create, analyze, and implement effective decision-making
models.

While most books on modern game theory are either too abstract
or too applied, this book provides a balanced treatment of the
subject that is both conceptual and hands-on. Game Theory
introduces readers to the basic theories behind games and presents
real-world examples from various fields of study such as economics,
political science, military science, finance, biological science as
well as general game playing. A unique feature of this book is the
use of Maple to find the values and strategies of games, and in
addition, it aids in the implementation of algorithms for the
solution or visualization of game concepts. Maple is also utilized
to facilitate a visual learning environment of game theory and acts
as the primary tool for the calculation of complex non-cooperative
and cooperative games.

Important game theory topics are presented within the following
five 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 Nucleolus
concept and the Shapley value

* Bargaining, including threat strategies

* Evolutionary stable strategies and population games

Although some mathematical competence is assumed, appendices are
provided to act as a refresher of the basic concepts of linear
algebra, probability, and statistics. Exercises are included at the
end of each section along with algorithms for the solution of the
games to help readers master the presented information. Also,
explicit Maple and Mathematica® commands are included in the
book and are available as worksheets via the book's related Web
site. The use of this software allows readers to solve many more
advanced and interesting games without spending time on the theory
of linear and nonlinear programming or performing other complex
calculations.

With extensive examples illustrating game theory's wide range of
relevance, this classroom-tested book is ideal for game theory
courses in mathematics, engineering, operations research, computer
science, and economics at the upper-undergraduate level. It is also
an ideal companion for anyone who is interested in the applications
of game theory.

Autor

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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 15.2.2011
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Technik
• Schlagworte: Ökonometrie • Angewandte Mathematik • Applied mathematics • Business & Finance • Econometrics • Economics • Finanzmathematik • Mathematics • Mathematik • Mathematik in Wirtschaft u. Finanzwesen • Ökonometrie • Volkswirtschaftslehre
• ISBN-10: 1-118-03065-6 / 1118030656
• ISBN-13: 978-1-118-03065-3 / 9781118030653