Invitation to Linear Programming and Game Theory

Written in a conversational tone, this classroom-tested text introduces the fundamentals of linear programming and game theory, showing readers how to apply serious mathematics to practical real-life questions by modelling linear optimization problems and strategic games. The treatment of linear programming includes two distinct graphical methods. The game theory chapters include a novel proof of the minimax theorem for 2x2 zero-sum games. In addition to zero-sum games, the text presents variable-sum games, ordinal games, and n-player games as the natural result of relaxing or modifying the assumptions of zero-sum games. All concepts and techniques are derived from motivating examples, building in complexity, which encourages students to think creatively and leads them to understand how the mathematics is applied. With no prerequisite besides high school algebra, the text will be useful to motivated high school students and undergraduates studying business, economics, mathematics, and the social sciences.

• 550 exercises and 110 worked examples
• Provides step-by-step instructions for using Wolfram Mathematica and Microsoft Excel to solve linear optimization problems and constant-sum games
• Introduces different techniques throughout the text so readers can easily compare them and develop intuition regarding which techniques are appropriate for which type of question
• Accommodates readers from different backgrounds by indicating what should be worked through or skipped depending on the reader's previous mathematical experience