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The geometry of efficient fair division /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The geometry of efficient fair division // Julius B. Barbanel ; with an introduction by Alan D. Taylor.
Author:	Barbanel, Julius B.,
other author:	Taylor, Alan D.,
Description:	1 online resource (ix, 462 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Partitions (Mathematics) -
Online resource:	https://doi.org/10.1017/CBO9780511546679
ISBN:	9780511546679 (ebook)

The geometry of efficient fair division /
Barbanel, Julius B.,1951-

The geometry of efficient fair division /Julius B. Barbanel ; with an introduction by Alan D. Taylor. - 1 online resource (ix, 462 pages) :digital, PDF file(s).

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Notation and preliminaries --Alan D. Taylor --Introduction /

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.

ISBN: 9780511546679 (ebook)Subjects--Topical Terms:

856957
Partitions (Mathematics)

LC Class. No.: QA165 / .B37 2005

Dewey Class. No.: 512.7/3

The geometry of efficient fair division /
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050 0 0 $a QA165 $b .B37 2005
082 0 0 $a 512.7/3 $2 22
100 1 $a Barbanel, Julius B., $d 1951- $e author. $3 1444055
245 1 4 $a The geometry of efficient fair division / $c Julius B. Barbanel ; with an introduction by Alan D. Taylor.
264 1 $a Cambridge : $b Cambridge University Press, $c 2005.
300 $a 1 online resource (ix, 462 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $g Introduction / $r Alan D. Taylor -- $g 1. $t Notation and preliminaries -- $g 2. $t Geometric object #1a : the individual pieces set (IPS) for two players -- $g 3. $t What the IPS tells us about fairness and efficiency in the two-player context -- $g 4. $t The individual pieces set (IPS) and the full individual pieces set (FIPS) for the general n-player context -- $g 5. $t What the IPS and the FIPS tell us about fairness and efficiency in the general n-player context -- $g 6. $t Characterizing Pareto optimality : introduction and preliminary ideas -- $g 7. $t Characterizing Pareto optimality I : the IPS and optimization of convex combinations of measures -- $g 8. $t Characterizing Pareto optimality II : partition ratios -- $g 9. $t Geometric object #2 : the Radon-Nikodym set (RNS) -- $g 10. $t Characterizing Pareto optimality III : the RNS, Weller's construction, and w-association -- $g 11. $t The shape of the IPS -- $g 12. $t The relationship between the IPS and the RNS -- $g 13. $t Other issues involving Weller's construction, partition ratios, and Pareto optimality -- $g 14. $t Strong Pareto optimality -- $g 15. $t Characterizing Pareto optimality using hyperreal numbers -- $g 16. $t Geometric object #1d : the multicake individual pieces set (MIPS) symmetry restored.
520 $a 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.
650 0 $a Partitions (Mathematics) $3 856957
700 1 $a Taylor, Alan D., $d 1947- $e writer of introduction. $3 1444056
776 0 8 $i Print version: $z 9780521842488
856 4 0 $u https://doi.org/10.1017/CBO9780511546679