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

Author(s): Steven J. Brams; Alan D. Taylor; William S. Zwicker
Journal: Proc. Amer. Math. Soc. 125 (1997), 547-554.
MSC (1991): Primary 90D10; Secondary 62C20
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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:

[A]
A. K. Austin, ``Sharing a cake'', Mathematical Gazette 6, no. 437 (October 1982), 212-215.

[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

[BTZ]
S. J. Brams, A. D. Taylor, and W. S. Zwicker, ``Old and new moving-knife schemes'', Mathematical Intelligencer 17, no. 4 (Fall, 1995). CMP 96:05

[N]
J. Neyman, ``Un theoreme d'existe'', C. R. Acad. Sci. Paris 222 (1946), 843-845. MR 7:457h

[S]
H. Steinhaus, ``The problem of fair division'', Econometrica 16, no. 1 (January 1948), 101-104.

[St]
W. Stromquist, ``How to cut a cake fairly'', American Mathematical Monthly 87, no. 8 (October 1980), 640-644. Addendum, vol. 88, no. 8 (October 1981), 613-614. MR 81m:05016

[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
Email: brams@is2.nyu.edu

Alan D. Taylor
Affiliation: Department of Mathematics, Union College, Schenectady, New York 12308
Email: taylora@gar.union.edu

William S. Zwicker
Affiliation: Department of Mathematics, Union College, Schenectady, New York 12308
Email: zwickerw@gar.union.edu

DOI: 10.1090/S0002-9939-97-03614-9
PII: S 0002-9939(97)03614-9
Received by editor(s): December 20, 1994
Received by editor(s) in revised form: August 29, 1995
Communicated by: Andreas R. Blass
Copyright of article: Copyright 1997, American Mathematical Society

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