Customer Reviews

Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis (Econometric Society Monographs)

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This book is totally dedicated to matching theory. The book in itself is rather general, it doesn't focus on any particular application, and discusses matching as a general abstract theory. Therefore the book can be used by both micro- and macro people equally. It basically covers the problem of one-to-one and one-to-many matchings and tries to explain when equilibriums exist and if matches are unique or non-unique and comes with algorithms or constructive methods to actually do the matching. The structure of the book is mostly like math books and at each step presents an algorithm or a theorem or lemma that states a result. In most cases the proof comes afterwards. However this doesn't undermine the practicality of the book as you can easily locate the algorithm or theorem that embodies your required result and just use it. In my opinion this is one of those books you want to keep on your shelf and refer to every now and then when need be.

This is a tightly focused book for academics interested in game-theoretic models of systems in which people are matched to either a) other people (as in the famous "Marriage Problem" elucidated by Gale and Shapley in their celebrated 1962 paper) or b) organizations (as in many school districts, college room draws and, most famously, several medical residency systems since the 1940s).

The lead author, Al Roth, has impeccable credentials: A Harvard economist, he's prolifically published in this field for more than two decades. In addition to his theoretical work, he's helped the Boston school system to redesign their matching algorithms, and, perhaps most impressively, engineered the New England Program for Kidney Exchange (NEPKE), which allows people to trade kidneys in a way that's both humane and efficient. In just a few years, the small program has saved dozens of lives, and is on track to expand elsewhere. (I had the pleasure of seeing Al Roth speak about this accomplishment.) Although Roth's work is technical in nature, he has never been excessive in his use of mathematical formalism, and that shows in this clear and concise graduate-level book.

NEPKE proves that there are still novel ways in which matching mechanisms can be applied to improve peoples' quality of life. This book offers an accessible entry point for this critical area of study.