2 Search Results for "Stromquist, Walter"


Document
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.

Cite as

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-dev.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}
}
Document
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)


Copy BibTex To Clipboard

@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-dev.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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