Insights into Game Theory: An Alternative Mathematical Experience

Michael Maschler z"l was one of the best teachers that I have ever had (I took his "differential equations" course in Spring 1972).He was also a legend among high school students, for his engaging outreach lectures that he gave from time to time, and indeed was very interestedin all levels of mathematics education. When I came across this introduction to Game Theory, I had very high expectations.I am glad to say that this book even exceeded them! Maschler must have transmitted his exceptional pedagogical talents to his disciple, Ein-Ya Gura.Together they produced a masterpiece of pedagogy that would appeal to a very wide range of potential readers, from the bright high school studentall the way to the non-expert professional mathematician. Even game-theorists would find a new perspective to familiar material, and this book would help themto better present this material to their students. This book can also serve as a paradigm for future text-book writing, and shows how one canbe rigorous without being pedantic, engaging without being frivolous, and the many beautifully chosen exercises will guarantee that students willactually learn to do mathematics, and slowly, but surely, digest very sophisticated material that earned Nobel prizes to their discoverers.

This is an unusual beginner's textbook in Game Theory. Unlike most of the books in the same category, this one focuses on topics other than non-cooperative games and their solutions. Without apparent effort, Professors Gura and Maschler (who regrettably passed away in 2008), present and explain in surprising detail key ideas in disparate fields like social choice theory, matching theory, cooperative game theory and the analysis of division problems. The most extraordinary accomplishment of this book is that it could be read with ease by smart high school students, notwithstanding the depth and rigor of its arguments.I've added this book as a mandatory text in my undergrad course on game theory. I can attest how engaging were its arguments for my students and how happy they were for being able to understand deep ideas (Arrow's Theorem, Shapley's Index, etc.). I even believe that the kids really enjoyed solving the exercises!So, my recommendation is: if you have to teach a college level course on game theory or just need a rapid yet sound introduction to the aforementioned topics, this is a book you need.

The auhtor took great pains to describe the details of game theory and their proofs of theorems are rock solid, ever single step in the proofs are explained carefully, without any handwaving. There are also plenty of exercises to help readers better understand the subject.I think this book sets the standard for how math/computer science books should be written.