Insights into Game Theory: An Alternative Mathematical Experience by Ein-Ya Gura (PDF)

Description

Few branches of mathematics have been more influential in the social sciences than game theory. In recent years, it has become an essential tool for all social scientists studying the strategic behaviour of competing individuals, firms and countries. However, the mathematical complexity of game theory is often very intimidating for students who have only a basic understanding of mathematics. Insights into Game Theory addresses this problem by providing students with an understanding of the key concepts and ideas of game theory without using formal mathematical notation. The authors use four very different topics (college admission, social justice and majority voting, coalitions and co-operative games, and a bankruptcy problem from the Talmud) to investigate four areas of game theory. The result is a fascinating introduction to the world of game theory and its increasingly important role in the social sciences.

User’s Reviews

Editorial Reviews: Review “This beautiful textbook adds a new tool to the ‘mathematical toolbox’ that is game theory: to be used in the treatment of a ‘fear of mathematics.’ Starting with interesting real-life questions, it provides the reader with an excellent training in mathematical thinking and reasoning, without her or him even noticing it. It is a remarkable achievement in mathematics teaching, empirically tested in classrooms by the authors.” Shmuel Zamir, Professor, Center for the Study of Rationality, The Hebrew University of Jerusalem“I wish I could have read this book when I was in high school. It is a marvelous introduction to some topics in game theory for the mathematically inclined reader that does not require extensive mathematical training. The topics are interesting and engage the reader. The presentation allows the reader to work through the logic of the arguments and see how they could be extended beyond the examples in the book.” – James D. Morrow, Professor of Political Science and Research Professor at the Center for Political Studies, University of Michigan“Game theory is becoming a major framework for analyzing competition and cooperation in the social sciences. Gura and Maschler’s book provides a wonderful perspective on the utility of game theory in social sciences by analyzing problems of justice, matching and more. The analysis is presented in a very appealing way so that every student can understand it. This unique book is an excellent addition to the literature on game theory.” Zur Shapira, William Berkley Professor of Entrepreneurship and Professor of Management, Stern School of Business, New York University”The authors’ approach to presenting material is exactly right. The book will help students make the first step into studying mathematical analysis of strategic behavior. An important addition to the literature on game theory.” J. Brzezinski, DePaul University for Choice Magazine Book Description A fascinating introduction to the key concepts and ideas of game theory. About the Author Ein-Ya Gura is Senior Lecturer in the Rothberg International School and a member of the Center for the Study of Rationality at the Hebrew University of Jerusalem.Michael B. Maschler is Professor of Mathematics and a member of the Center for the Study of Rationality at the Hebrew University of Jerusalem. Professor Maschler is one of the most distinguished game theorists in the world. With Robert Aumann (co-winner of the 2005 Nobel Prize for Economics), he solved a 2000-year-old puzzle on inheritance laws in the Talmud. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This has to be the most accessible introduction to Cooperative Game Theory ever.

⭐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.

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