Thie / Keough An Introduction to Linear Programming and Game Theory

3. Auflage 2011
ISBN: 978-1-118-16545-4
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 480 Seiten, E-Book

Praise for the Second Edition:
"This is quite a well-done book: very tightly organized,better-than-average exposition, and numerous examples,illustrations, and applications."
--Mathematical Reviews of the American MathematicalSociety
An Introduction to Linear Programming and Game Theory, ThirdEdition presents a rigorous, yet accessible, introduction tothe theoretical concepts and computational techniques of linearprogramming and game theory. Now with more extensive modelingexercises and detailed integer programming examples, this bookuniquely illustrates how mathematics can be used in real-worldapplications in the social, life, and managerial sciences,providing readers with the opportunity to develop and apply theiranalytical abilities when solving realistic problems.
This Third Edition addresses various new topics and improvementsin the field of mathematical programming, and it also presents twosoftware programs, LP Assistant and the Solver add-in for MicrosoftOffice Excel, for solving linear programming problems. LPAssistant, developed by coauthor Gerard Keough, allows readers toperform the basic steps of the algorithms provided in the book andis freely available via the book's related Web site. The use of thesensitivity analysis report and integer programming algorithm fromthe Solver add-in for Microsoft Office Excel is introduced soreaders can solve the book's linear and integer programmingproblems. A detailed appendix contains instructions for the use ofboth applications.
Additional features of the Third Edition include:
* A discussion of sensitivity analysis for the two-variableproblem, 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 ofthe dual problem
* A section on developing an example in Data EnvelopmentAnalysis
* An outline of the proof of John Nash's theorem on the existenceof equilibrium strategy pairs for non-cooperative, non-zero-sumgames
Providing a complete mathematical development of all presentedconcepts and examples, Introduction to Linear Programming andGame Theory, Third Edition is an ideal text for linearprogramming and mathematical modeling courses at theupper-undergraduate and graduate levels. It also serves as avaluable reference for professionals who use game theory inbusiness, economics, and management science.

Autoren/Hrsg.

Thie, Paul R.

Keough, Gerard E.

Inhaltsverzeichnis

Preface xi
1 Mathematical Models 1
1.1 Applying Mathematics 1
1.2 The Diet Problem 2
1.3 The Prisoner's Dilemma 5
1.4 The Roles of Linear Programming and Game Theory 8
2 The Linear Programming Model 9
2.1 History 9
2.2 The Blending Model 10
2.3 The Production Model 21
2.4 The Transportation Model 34
2.5 The Dynamic Planning Model 38
2.6 Summary 47
3 The Simplex Method 57
3.1 The General Problem 57
3.2 Linear Equations and Basic Feasible Solutions 63
3.3 Introduction to the Simplex Method 72
3.4 Theory of the Simplex Method 77
3.5 The Simplex Tableau and Examples 85
3.6 Artificial Variables 93
3.7 Redundant Systems 101
3.8 A Convergence Proof 106
3.9 Linear Programming and Convexity 110
3.10 Spreadsheet Solution of a Linear Programming Problem 115
4 Duality 121
4.1 Introduction to Duality 121
4.2 Definition of the Dual Problem 123
4.3 Examples and Interpretations 132
4.4 The Duality Theorem 138
4.5 The Complementary Slackness Theorem 154
5 Sensitivity Analysis 161
5.1 Examples in Sensitivity Analysis 161
5.2 Matrix Representation of the Simplex Algorithm 175
5.3 Changes in the Objective Function 183
5.4 Addition of a New Variable 189
5.5 Changes in the Constant-Term Column Vector 192
5.6 The Dual Simplex Algorithm 196
5.7 Addition of a Constraint 204
6 Integer Programming 211
6.1 Introduction to Integer Programming 211
6.2 Models with Integer Programming Formulations 214
6.3 Gomory's Cutting Plane Algorithm 228
6.4 A Branch and Bound Algorithm 237
6.5 Spreadsheet Solution of an Integer Programming Problem 244
7 The Transportation Problem 251
7.1 A Distribution Problem 251
7.2 The Transportation Problem 264
7.3 Applications 282
8 Other Topics in Linear Programming 299
8.1 An Example Involving Uncertainty 299
8.2 An Example with Multiple Goals 306
8.3 An Example Using Decomposition 314
8.4 An Example in Data Envelopment Analysis 325
9 Two-Person, Zero-Sum Games 337
9.1 Introduction to Game Theory 337
9.2 Some Principles of Decision Making in Game Theory 345
9.3 Saddle Points 350
9.4 Mixed Strategies 353
9.5 The Fundamental Theorem 360
9.6 Computational Techniques 370
9.7 Games People Play 382
10 Other Topics in Game Theory 391
10.1 Utility Theory 391
10.2 Two-Person, Non-Zero-Sum Games 393
10.3 Noncooperative Two-Person Games 397
10.4 Cooperative Two-Person Games 404
10.5 The Axioms of Nash 408
10.6 An Example 414
A Vectors and Matrices 417
B An Example of Cycling 421
C Efficiency of the Simplex Method 423
D LP Assistant 427
E Microsoft Excel and Solver 431
Bibliography 439
Solutions to Selected Problems 443
Index 457

Über Autor(innen)

PAUL R. THIE, PhD, is Professor Emeritus in the Department of Mathematics at Boston College. Dr. Thie has authored numerous journal articles in the areas of mathematical programming and several complex variables.
GERARD E. KEOUGH, PhD, is Associate Professor and former chair of the Department of Mathematics at Boston College. He has written extensively on operator theory, functional analysis, and the use of technology in mathematics. Dr. Keough is the coauthor of Getting Started with Maple, Second Edition and Getting Started with Mathematica, Second Edition, both published by Wiley.