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)


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.
  • Cake cutting
  • pie cutting
  • envy free


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