Cake division with minimal cuts: Envy-free procedures for three persons, four persons, and beyond

Mathematical social sciences

Volumn 48, Issue 3, 2004, Pages 251-269

  Barbanel, Julius B ^a   Brams, Steven J ^b  

^a UNION COLLEGE   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Cake cutting; Envy freeness; Fair division; Minimal cuts; Moving knife algorithm

Indexed keywords

EID: 5444259326     PISSN: 01654896     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mathsocsci.2004.03.006     Document Type: Article

References (24)

1. Barbanel J.B. The Geometry of Efficient Fair Division 2004 Cambridge Univ. Press
2. Brams S.J. Kilgour D.M. Competitive fair division Journal of Political Economy 109 2 2001 418-443 (April)
3. Brams S.J. Taylor A.D. An envy-free cake division protocol American Mathematical Monthly 102 1 1995 9-18 (January)
4. Brams S.J. Taylor A.D. Fair Division: From Cake-Cutting to Dispute Resolution 1996 Cambridge Univ. Press New York
5. Brams S.J. Taylor A.D. The Win-Win Solution: Guaranteeing Fair Shares to Everybody 1999 W.W. Norton New York
6. Brams S.J. Taylor A.D. Zwicker W.S. Old and new moving-knife schemes Mathematical Intelligencer 17 4 1995 30-35 (Fall)
7. Brams S.J. Taylor A.D. Zwicker W.S. A moving-knife solution to the four-person envy-free cake division problem Proceedings of the American Mathematical Society 125 2 1997 547-554 (February)
8. Brams S.J. Jones M.A. Klamler C. Perfect Cake-Cutting Procedures with Money 2004 Department of Politics, New York University Preprint
9. Dubins L.E. Spanier E.H. How to cut a cake fairly American Mathematical Monthly 68 1 1961 1-17 (January)
10. Even S. Paz A. A note on cake cutting Discrete Applied Mathematics 7 1984 285-296
11. Gale D. Mathematical entertainments Mathematical Intelligencer 15 1 1993 48-52 (Winter)
12. Ichiishi T. Idzik A. Equitable allocation of divisible goods Journal of Mathematical Economics 32 1999 389-400
13. Jones M.A. Equitable, envy-free, and efficient cake cutting for two people and its application to divisible goods Mathematics Magazine 75 4 2002 275-283 (October)
14. Moulin H.J. Fair Division and Collective Welfare 2003 MIT Press Cambridge, MA
15. Peterson E. Su F.E. Four-person envy-free chore division Mathematics Magazine 75 2 2000 117-122 (April)
16. Pikhurko O. On envy-free cake division American Mathematical Monthly 107 8 2000 736-738 (October)
17. Robertson J.M. Webb W.A. Near exact and envy-free cake division Ars Combinatoria 45 1997 97-108
18. Robertson J. Webb W. Cake-Cutting Algorithms: Be Fair If You Can 1998 A K Peters Natick, MA
19. Shishido H. Zeng D.-Z. Mark-choose-cut algorithms for fair and strongly fair division Group Decision and Negotiation 8 2 1999 125-137 (March)
20. Stromquist W. How to cut a cake fairly American Mathematical Monthly 87 8 1980 640-644 (October)
21. Su F.E. Rental harmony: Sperner's lemma in fair division American Mathematical Monthly 106 1999 922-934
22. Woodall D.R. Dividing a cake fairly Journal of Mathematical Analysis and Applications 78 1 1980 233-247 (November)
23. Young H.P. Equity in Theory and Practice 1994 Princeton Univ. Press Princeton, NJ
24. Zeng D.-Z. Approximate envy-free procedures Game Practice: Contributions from Applied Game Theory 2000 259-271 Kluwer Academic Publishing Dordrecht, The Netherlands