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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/
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Brams, Steven J. ; Jones, Michael A. ; Klamler, Christian

Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure

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07261.BramsSteven.Paper.1221.pdf (0.2 MB)


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
Collection: 07261 - Fair Division
Issue Date: 2007
Date of publication: 26.11.2007


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