When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07261.3
URN: urn:nbn:de:0030-drops-12192
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Stromquist, Walter

A Pie That Can't Be Cut Fairly (revised for DSP)

07261.StromquistWalter.Paper.1219.pdf (0.1 MB)


David Gale asked (Math. Intel. 1993) whether, when a pie is to be divided among n claimants, it is always possible to find a division that is both envy free and undominated. The pie is cut along n radii and the claimants' preferences are described by separate measures.

We answer Gale's question in the negative for n=3 by exhibiting three measures on a pie such that, when players have these measures, no division of the pie can be both envy free and undominated. The measures assign positive values to pieces with positive area.

BibTeX - Entry

  author =	{Stromquist, Walter},
  title =	{{A Pie That Can't Be Cut Fairly (revised for DSP)}},
  booktitle =	{Fair Division},
  pages =	{1--10},
  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 =		{},
  URN =		{urn:nbn:de:0030-drops-12192},
  doi =		{10.4230/DagSemProc.07261.3},
  annote =	{Keywords: Cake cutting, pie cutting, envy free}

Keywords: Cake cutting, pie cutting, envy free
Collection: 07261 - Fair Division
Issue Date: 2007
Date of publication: 26.11.2007

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