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

Author Walter Stromquist



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Walter Stromquist

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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

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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