Cutting a Pie Is Not a Piece of Cake

@article{Barbanel2009CuttingAP,
  title={Cutting a Pie Is Not a Piece of Cake},
  author={Julius B. Barbanel and Steven J. Brams and Walter Stromquist},
  journal={The American Mathematical Monthly},
  year={2009},
  volume={116},
  pages={496-514}
}
Gale (1993) posed the question of whether there is necessarily an undominated, envy-free allocation of a pie when it is cut into wedge-shaped pieces or sectors. For two players, we give constructive procedures for obtaining such an allocation, whether the pie is cut into equal-size sectors by a single diameter cut or into two sectors of unequal size. Such an allocation, however, may not be equitable—that is, give the two players exactly the same value from their pieces. For three players, we… CONTINUE READING

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