DagSemProc.07261.3.pdf
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A Pie That Can't Be Cut Fairly (revised for DSP)
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Dagstuhl Seminar Proceedings, Volume 7261
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2007-11-26
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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)
https://doi.org/10.4230/DagSemProc.07261.3
https://doi.org/10.4230/DagSemProc.07261.3
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.
Keywords
- Cake cutting
- pie cutting
- envy free
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