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DOI: 10.4230/DagSemProc.07261.6
URN: urn:nbn:de:0030-drops-12211
URL: https://drops.dagstuhl.de/opus/volltexte/2007/1221/
Brams, Steven J. ; Jones, Michael A. ; Klamler, Christian
Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure
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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:DagSemProc.07261.6,
author = {Brams, Steven J. and Jones, Michael A. and Klamler, Christian},
title = {{Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure}},
booktitle = {Fair Division},
pages = {1--31},
series = {Dagstuhl Seminar Proceedings (DagSemProc)},
ISSN = {1862-4405},
year = {2007},
volume = {7261},
editor = {Steven Brams and Kirk Pruhs and Gerhard Woeginger},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2007/1221},
URN = {urn:nbn:de:0030-drops-12211},
doi = {10.4230/DagSemProc.07261.6},
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 |
