The Geometry of Efficient Fair Division

Julius B. Barbanel and Alan D. Taylor

Published by Cambridge University Press, 2009
ISBN 10: 051154667X / ISBN 13: 9780511546679
Used / Printed Access Code / Quantity Available: 0
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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.

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.

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Title: The Geometry of Efficient Fair Division
Publisher: Cambridge University Press
Publication Date: 2009
Binding: Printed Access Code
Book Condition: Used: Good

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Julius B. Barbanel
Published by Cambridge University Press (2009)
ISBN 10: 051154667X ISBN 13: 9780511546679
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Book Description Cambridge University Press, 2009. Printed Access Code. Book Condition: New. book. Bookseller Inventory # M051154667X

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