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

Review:

'In Chapters 12 and 13, he studies the relationship between the IPS and the RNS, and he provides a new presentation of the fundamental result that ensures the existence of a partition that is both Pareto optimal and envy-free.' Zentralblatt MATH

Book Description:

The author 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 several results concerning efficiency properties such as Pareto maximality and fairness properties such as envy-freeness for partitions.

About this edition

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