Brickman L. Mathematical Introduction to Linear Programming and Game Theory 1998

Textbook in PDF format

Mathematical elegance is a constant theme in this treatment of linear programming and matrix games. Condensed tableaus, minimal in size and notation, are employed for the simplex algorithm. In the context of these tableaus the beautiful termination theorem of RG 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