Author(s): Julius B. Barbanel (Author), Alan D. Taylor (Introduction)
Publisher: Cambridge University Press
Publication Date: January 24, 2005
Edition: 1st
Language: English
Print length: 472 pages
ISBN-10: 0521842484
ISBN-13: 9780397515851
Book Description
What is the best way to divide a cake and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players generally using different measures. The author investigates efficiency properties (is there another partition that would make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (do all players think that their piece is at least as large as every other player’s piece?). He focuses exclusively on abstract existence results rather than algorithms, and on the geometric objects that arise naturally in this context. By examining the shape of these objects and the relationship between them, he demonstrates results concerning the existence of efficient and fair partitions.
Editorial Reviews
Review
“The monograph is a clearly-written, matter-of-fact presentation of definitions, theorems, and proofs.” MAA Reviews, Stephen Ahearn, Macalester College
“The main virtue of the book is the depth at which the author studies the division problem while maintaining the breadth across the mathematical sciences and the mathematical elegance with which he presents the results. The book should be of special interest not only to mathematicians and mathematical scientists but also to graduate students and researchers in management science, operations research, and system science who study resource allocation, optimization and decision making.” Margaret M. Wiecek, MATHEMATICAL REVIEWS
Book Description
Investigates efficiency properties such as Pareto maximality and fairness properties such as envy-freeness in a geometric context.
About the Author
Julius B. Barbanel is Professor of Mathematics at Union College, where he has also served as Department Chair. He has published numerous articles in the areas of both Logic and Set Theory, and Fair Division in leading mathematical journals. He is a member of the Mathematical Association of American, the Association of Symbolic Logic, and the Game Theory Society.
Wow! eBook
