Brams, Steven J. ;
Jones, Michael A. ;
Klamler, Christian
Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure
Abstract
Properties of discrete cake-cutting procedures that use a minimal number of cuts (n – 1 if there are n players) are analyzed. None is always envy-free or efficient, but divide-and-conquer (D&C) minimizes the maximum number of players that any single player may envy. It works by asking n ? 2 players successively to place marks on a cake that divide it into equal or approximately equal halves, then halves of these halves, and so on. Among other properties, D&C (i) ensures players of more than 1/n shares if their marks are different and (ii) is strategyproof for risk-averse players. However, D&C may not allow players to obtain proportional, connected pieces if they have unequal entitlements. Possible applications of D&C to land division are briefly discussed.
BibTeX - Entry
@InProceedings{brams_et_al:DSP:2007:1221,
author = {Steven J. Brams and Michael A. Jones and Christian Klamler},
title = {Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure},
booktitle = {Fair Division},
year = {2007},
editor = {Steven Brams and Kirk Pruhs and Gerhard Woeginger},
number = {07261},
series = {Dagstuhl Seminar Proceedings},
ISSN = {1862-4405},
publisher = {Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2007/1221},
annote = {Keywords: Cake-cutting, proportionality, envy-freeness, efficiency, strategy-proofness}
}
|
Keywords: |
|
Cake-cutting, proportionality, envy-freeness, efficiency, strategy-proofness |
|
Seminar: |
|
07261 - Fair Division
|
|
Issue date: |
|
2007 |
|
Date of publication: |
|
26.11.2007 |
