Cake-Cutting Algorithms: Be Fair if You Can

by Jack Robertson, William Webb

The challenge of dividing an asset fairly, from cakes to more important properties, is of great practical importance in many situations. Since the famous Polish school of mathematicians (Steinhaus, Banach, and Knaster) introduced and described algorithms for the fair division problem in the 1940s, the concept has been widely popularized. This book gathers into one readable and inclusive source a comprehensive discussion of the state of the art in cake-cutting problems for both the novice and the professional. It offers a complete treatment of all cake-cutting algorithms under all the considered definitions of "fair" and presents them in a coherent, reader-friendly manner. Robertson and Webb have brought this elegant problem to life for both the bright high school student and the professional researcher.

Genres: Mathematics, Economics

177 pages, Hardcover

First published March 1, 1998

Reviews

[Frank · Rating 4 out of 5]

What do you expect from a book on mathematics?

1) It should be accessible, but not trivial.
2) The concepts should by well motivated and clearly explained. (CCA consistently introduces difficult proofs - of which there are a fair share in the later chapters - with a motivational prelude).
3) It should open the way to new lines of thought.

Books meeting points 2) and 3) are hard enough to come by, but point 1) may be the most difficult of all, as the constraints apply to nearly complementary sets.

CCA meets all three criteria, although this book arguably belongs on the (micro-)economics shelf, not with the math books.

[Aaron · Rating 5 out of 5]

An absolutely delightful ride through the mathematics of how to fairy share resources. The only real drawback is that the book is ten years old, so people really interested in the subject would want to further explore the contemporary research. Don't worry about not having the needed mathematical background, gentle reader; if you can follow any sort of college-level proof, you can at least get through the first seven chapters.