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

Authors: Walter Stromquist

Published in: Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007)

Abstract

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.

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Walter Stromquist. A Pie That Can't Be Cut Fairly (revised for DSP). In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{stromquist:DagSemProc.07261.3,
  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 =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.3},
  URN =		{urn:nbn:de:0030-drops-12192},
  doi =		{10.4230/DagSemProc.07261.3},
  annote =	{Keywords: Cake cutting, pie cutting, envy free}
}

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DOI: 10.4230/DagSemProc.07261.8

Envy-free cake divisions cannot be found by finite protocols

Authors: Walter Stromquist

Published in: Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007)

Abstract

No finite protocol (even if unbounded) can guarantee an envy-free division of a cake among three or more players, if each player is to receive a single connected piece.

Cite as

Walter Stromquist. Envy-free cake divisions cannot be found by finite protocols. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{stromquist:DagSemProc.07261.8,
  author =	{Stromquist, Walter},
  title =	{{Envy-free cake divisions cannot be found by finite protocols}},
  booktitle =	{Fair Division},
  pages =	{1--9},
  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/entities/document/10.4230/DagSemProc.07261.8},
  URN =		{urn:nbn:de:0030-drops-12208},
  doi =		{10.4230/DagSemProc.07261.8},
  annote =	{Keywords: Cake cutting, envy free, finite protocol}
}

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Documents authored by Stromquist, Walter

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

Abstract

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Envy-free cake divisions cannot be found by finite protocols

Abstract

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