Cutting a Pie Is Not a Piece of Cake

  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},
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

From This Paper

Figures, tables, and topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 15 references

“ Mathematical Entertainments . ”

  • David Gale
  • Mathematical Intelligencer
  • 1993
Highly Influential
4 Excerpts

Cake Division with Minimal Cuts : EnvyFree Procedures for 3 Persons , 4 Persons , and Beyond

  • M. Jones S. Brams, C. Klamler
  • Mathematical Social Sciences
  • 2004

Sperner ’ s Lemma in Fair Division

  • F. E. Su
  • American Mathematical Monthly
  • 1999

A MovingKnife Solution to the Four - Person EnvyFree Cake Division Problem

  • A. Taylor S. Brams, W. Zwicker
  • Proceedings of the American Mathematical Society
  • 1997

Proportional PieCutting

  • S. Brams, A. Taylor
  • Fair Division : From CakeCutting to Dispute…
  • 1996
2 Excerpts

Similar Papers

Loading similar papers…