An Introduction to Linear Programming and Game Theory / Edition 2

An Introduction to Linear Programming and Game Theory / Edition 2

by Paul R. Thie
     
 

ISBN-10: 0471624888

ISBN-13: 9780471624882

Pub. Date: 03/28/1988

Publisher: Wiley

An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in

Overview

An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems.

This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications.

Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models, Revised proofs and a discussion on the relevance and solution of the dual problem, A section on developing an example in Data Envelopment Analysis, An outline of the proof of John Nash's theoremon the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games.

Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.

About the Author:
Paul R. Thie, PhD, is Professor Emeritus in the Department of Mathematics at Boston College

About the Author:
Gerard E. Keough, PhD, is Associate Professor and former chair of the Department of Mathematics at Boston College

Product Details

ISBN-13:
9780471624882
Publisher:
Wiley
Publication date:
03/28/1988
Edition description:
Older Edition
Pages:
416
Product dimensions:
6.44(w) x 9.57(h) x 1.30(d)

Table of Contents


Preface     xi
Mathematical Models     1
Applying Mathematics     1
The Diet Problem     2
The Prisoner's Dilemma     5
The Roles of Linear Programming and Game Theory     8
The Linear Programming Model     9
History     9
The Blending Model     10
The Production Model     21
The Transportation Model     34
The Dynamic Planning Model     38
Summary     47
The Simplex Method     57
The General Problem     57
Linear Equations and Basic Feasible Solutions     63
Introduction to the Simplex Method     72
Theory of the Simplex Method     77
The Simplex Tableau and Examples     85
Artificial Variables     93
Redundant Systems     101
A Convergence Proof     106
Linear Programming and Convexity     110
Spreadsheet Solution of a Linear Programming Problem     115
Duality     121
Introduction to Duality     121
Definition of the Dual Problem     123
Examples and Interpretations     132
The Duality Theorem     138
The Complementary Slackness Theorem     154
Sensitivity Analysis     161
Examples in Sensitivity Analysis     161
Matrix Representation of the Simplex Algorithm     175
Changes in the Objective Function     183
Addition of a New Variable     189
Changes in the Constant-Term Column Vector     192
The Dual Simplex Algorithm     196
Addition of a Constraint     204
Integer Programming     211
Introduction to Integer Programming     211
Models with Integer Programming Formulations     214
Gomory's Cutting Plane Algorithm     228
A Branch and Bound Algorithm     237
Spreadsheet Solution of an Integer Programming Problem     244
The Transportation Problem     251
A Distribution Problem     251
The Transportation Problem     264
Applications     282
Other Topics in Linear Programming     299
An Example Involving Uncertainty     299
An Example with Multiple Goals     306
An Example Using Decomposition     314
An Example in Data Envelopment Analysis     325
Two-Person, Zero-Sum Games     337
Introduction to Game Theory     337
Some Principles of Decision Making in Game Theory     345
Saddle Points     350
Mixed Strategies     353
The Fundamental Theorem     360
Computational Techniques     370
Games People Play     382
Other Topics in Game Theory     391
Utility Theory     391
Two-Person, Non-Zero-Sum Games     393
Noncooperative Two-Person Games     397
Cooperative Two-Person Games     404
The Axioms of Nash     408
An Example     414
Vectors and Matrices     417
An Example of Cycling     421
Efficiency of the Simplex Method     423
LP Assistant     427
Microsoft Excel and Solver     431
Bibliography     439
Solutions to Selected Problems     443
Index     457

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