Insights into Game Theory: An Alternative Mathematical Experience

by Ein-Ya Gura, Michael Maschler

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.

Genres: Mathematics, Economics, Business

252 pages, Hardcover

First published July 1, 2008

Reviews

[Phil Filippak · Rating 3 out of 5]

Although only in the field of cooperative game theory, the topics choice is great. Explanation is mediocre. But examples and exercises are repetitive and monotonous. That doesn't do any good to the book, and completing indistinguishable problems would be too wasteful of time.

[Naessens · Rating 2 out of 5]

As far as I am concerned, I do not consider this book a proper introduction to Game Theory in so far as it lacks the basic vocabulary or elementary concepts such as players, strategy or Nash-equilibrium.

The first chapter is the most interesting in my opinion. It deals with finding the best matching between two groups (e.g. schools-students, men-women) also known as the stable marriage problem. It is well-written, well-paced and introduces the Gale-Shapley algorithm.
The second chapter is also interesting, but I find it a little less readable. It is about social-justice and after defining which properties social justice should abide by, it comes to the disillusioning conclusion that social justice and democracy are not always compatible ! Good to know, but sad.
I find chapter 3 confusing. I have read better explanations of the Shapley values and better descriptions of cooperative games. Furthermore, the concept of core-value is not mentioned ; but it's OK for a book that is supposed to give just insights into Game Theory.
The fourth and last chapter concerns the Talmud bankruptcy problem. Why spend so many pages on a non-intuitive distribution whereas the most intuitive allocation method (in my opinion) is relegated to paragraph 4.15 ?

The book has a lot of small exercises, a few have solutions at the end of the book. I try one, find a different solution and found no errata on the website. Strange.
For me Insights Into Game Theory: An Alternative Mathematical Experience is not a real introduction to Game Theory and has little to do with this domain. I'd rather recommend Introduction to Game Theory for newcomers. Everyone who has little interest or knowledge in game theory and wants to learn more should pick another book. However, I don't want to give the idea that the book is uninteresting : if you're interested in the Talmud bankruptcy issue or the Gale-Shapley applications or social justice, then go ahead and read the appropriate chapter.

[Alexis Bauer Kolak · Rating 3 out of 5]

This was an odd little book. It was like pop science if you stripped out all the analogies and quotations, then added an exercises section. I love the examples and appreciated the chance to test my ability to absorb the concepts (though the answer key did not totally match up). However, there was a lot of repetition, and not all of the examples were broken down step by step, so if you don't get the general concept, you can't use the example to parse it out. There are also a few points where a new concept is added but not explained (switching from unions to directional joins). Last item: a chapter on how this kind of analysis gets done in the real world would be helpful. Having to diagram stuff out by hand got old fast and isn't useful in real life.

[Danial Esmaeili · Rating 4 out of 5]

This is a well-written book in game theory with several real-life examples. The authors prevent to give sophisticated proves for theorems but they have tried to be clear-cut. The two penultimate and last chapters are written amazing. The only weakness of this book could be seen in the second chapter.

[Cain S. · Rating 4 out of 5]

This book is that rare thing: a discursive mathematics book which successfully communicates the context of application, while also explicitly teaching the computational skills required with great clarity.

[Yaqiao Li · Rating 5 out of 5]

succinct and clear in math.