Mathematical Introduction to Linear Programming and Game Theory

Description

Mathematical elegance is a constant theme in this treatment of linear programming and matrix games. Condensed tableau, minimal in size and notation, are employed for the simplex algorithm. In the context of these tableau the beautiful termination theorem of R.G. Bland is proven more simply than heretofore, and the important duality theorem becomes almost obvious. Examples and extensive discussions throughout the book provide insight into definitions, theorems, and applications. There is considerable informal discussion on how best to play matrix games. The book is designed for a one-semester undergraduate course. Readers will need a degree of mathematical sophistication and general tools such as sets, functions, and summation notation. No single college course is a prerequisite, but most students will do better with some prior college mathematics. This thorough introduction to linear programming and game theory will impart a deep understanding of the material and also increase the student's mathematical maturity. Front Matter....Pages i-xi Simultaneous Linear Equations....Pages 1-15 Linear Programming Foundations....Pages 16-31 The Simplex Algorithm....Pages 32-61 Dual Tableaux and Two-Phase Algorithms....Pages 62-75 Dual LP Problems....Pages 76-94 Matrix Games....Pages 95-123 Back Matter....Pages 125-132