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.

'We all want to pull back the curtains for students, revealing a wider, more glorious mathematical universe beyond a mere list of rules for calculation. What content best introduces mathematics as the analysis of ideas that are both beautiful and essential to our understanding of the world? Everyone plays games whenever their goals contend against those of others, so our students already have experience with strategic reasoning. This helps Game Theory lower the abstraction barrier, making it an ideal context for a first course in mathematical reasoning. Vella's careful and thorough treatment uses clear language, in a conversational tone ideal for its intended audience: advanced high school students, along with first and second year undergraduates. What further distinguishes it from other texts is its parallel treatment of Linear Programming alongside Game Theory. This is a marriage made in heaven, with each topic serving the needs of the other.' William S. Zwicker, Union College, 'This volume could be used to support coursework fulfilling math requirements offered for students with non-mathematics majors such as business or economics, or to supplement linear algebra courses. Recommended.' J. Parker, Choice, 'This book is a scientific gift offered to the students by a genuine professor in linear mathematical programming and game theory, with proper applications.' Vasile Postolică, European Mathematical Society

David C. Vella is Professor and Associate Chair of Mathematics at Skidmore College, New York. He has taught college mathematics for over thirty-five years, and has been an organizer of the Hudson River Undergraduate Mathematics Conference (HRUMC) since its inception in 1993. He is a member of the AMS, the MAA, and a charter member of the New York Alpha Theta chapter of Pi Mu Epsilon. His Erdős number is four.