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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
MathSciNet review:
1353378
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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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