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A moving-knife solution to the four-person
envy-free cake-division problem

Authors: Steven J. Brams, Alan D. Taylor and William S. Zwicker
Journal: Proc. Amer. Math. Soc. 125 (1997), 547-554
MSC (1991): Primary 90D10; Secondary 62C20
MathSciNet review: 1353378
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Abstract | References | Similar Articles | Additional Information

Abstract: We present a moving-knife procedure, requiring only 11 cuts, that produces an envy-free allocation of a cake among four players and discuss possible extensions to five players.

References [Enhancements On Off] (What's this?)

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  • [BT 1] S. J. Brams and A. D. Taylor, ``An envy-free cake-division protocol'', American Mathematical Monthly 102, no. 1 (January 1995), 9-18. CMP 95:09
  • [BT 2] S. J. Brams and A. D. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution, Cambridge, UK: Cambridge University Press (1996). CMP 96:10
  • [BT 3] S. J. Brams and A. D. Taylor, ``A note on envy-free cake division'', Journal of Combinatorial Theory, Series A 70, no. 1 (April, 1995), 170-173. MR 96b:05014
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  • [W] W. Webb, ``But he got a bigger piece than I did'', preprint, n.d.

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Additional Information

Steven J. Brams
Affiliation: Department of Politics, New York University, New York, New York 10003

Alan D. Taylor
Affiliation: Department of Mathematics, Union College, Schenectady, New York 12308

William S. Zwicker

Received by editor(s): December 20, 1994
Received by editor(s) in revised form: August 29, 1995
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society

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