The Geometry of Efficient Fair Division - Hardcover

Barbanel, Julius B.

Hardcover

ISBN 10: 0521842484 ISBN 13: 9780521842488

Publisher: Cambridge University Press, 2005

Synopsis

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.

About this title

Book Description:

This book takes a geometric approach to the problem of Fair Division, focusing exclusively on abstract existence results rather than algorithms. The author investigates efficiency properties (such as: 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 (such as: Do all players think that their piece is at least as large as every other player's piece?). By examining the shape of geometric objects that can be naturally associated with Fair Division, and by studying the relationship between these objects, he demonstrates results concerning the existence of efficient and fair partitions.

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.

About this edition

• Publisher: Cambridge University Press
• Publication date: 2005
• ISBN 10: 0521842484
• ISBN 13: 9780521842488
• Binding: Hardcover
• Edition number: 1
• Number of pages: 472