Cake Cutting – Fair and Square
AbstractThe classic fair cake-cutting problem [Steinhaus, 1948] is extended by introducing geometric constraints on the allocated pieces. Specifically, agents may demand to get their share as a square or a rectangle with a bounded length/width ratio. This is a plausible constraint in realistic cake-cutting applications, notably in urban and agricultural economics where the “cake” is land. Geometric constraints greatly affect the classic results of the fair division theory. The existence of a proportional division, giving each agent 1/n of his total cake value, is no longer guaranteed. We prove that it is impossible to guarantee each agent more than 1/(2n-1) of his total value. Moreover, we provide procedures implementing partially proportional division, giving each agent 1/(An-B) of his total value, where A and B are constants depending on the shape of the cake and its pieces. Fairness and social welfare implications of these procedures are analyzed in various scenarios.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Bar-Ilan University, Department of Economics in its series Working Papers with number 2014-01.
Length: 44 pages
Date of creation: Jan 2014
Date of revision:
Contact details of provider:
Postal: Faculty of Social Sciences, Bar Ilan University 52900 Ramat-Gan
Phone: Phone: +972-3-5318345
Web page: http://www.biu.ac.il/soc/ec
More information through EDIRC
fair division; cake cutting; land division; geometry; non-additive utilities; social welfare;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2014-01-24 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dall'Aglio, Marco & Maccheroni, Fabio, 2009.
Games and Economic Behavior,
Elsevier, vol. 66(1), pages 57-77, May.
- Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216.
- Chen, Yiling & Lai, John K. & Parkes, David C. & Procaccia, Ariel D., 2013. "Truth, justice, and cake cutting," Games and Economic Behavior, Elsevier, vol. 77(1), pages 284-297.
- Moulin, Herve, 1990.
"Uniform externalities : Two axioms for fair allocation,"
Journal of Public Economics,
Elsevier, vol. 43(3), pages 305-326, December.
- Moulin, H., 1989. "Uniform Externalities: Two Axioms For Fair Allocation," UFAE and IAE Working Papers 117-89, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Fabio Maccheroni & Fabio Maccheroni & Massimo Marinacci & Massimo Marinacci, 2003.
"How to cut a pizza fairly: Fair division with decreasing marginal evaluations,"
Social Choice and Welfare,
Springer, vol. 20(3), pages 457-465, 06.
- Massimo Marinacci & Fabio Maccheroni, 2002. "How to cut a pizza fairly: fair division with descreasing marginal evaluations," ICER Working Papers - Applied Mathematics Series 23-2002, ICER - International Centre for Economic Research.
- Marco LiCalzi & Antonio Nicolo, 2007.
"Efficient Egalitarian Equivalent Allocations over a Single Good,"
152, Department of Applied Mathematics, Università Ca' Foscari Venezia.
- Marco LiCalzi & Antonio Nicolò, 2009. "Efficient egalitarian equivalent allocations over a single good," Economic Theory, Springer, vol. 40(1), pages 27-45, July.
- Marco LiCalzi & Antonio Nicolò, 2005. "Efficient Egalitarian Equivalent Allocations over a Single Good," Microeconomics 0510014, EconWPA.
- William Thomson, 2007. "Children Crying at Birthday Parties. Why?," Economic Theory, Springer, vol. 31(3), pages 501-521, June.
- Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061 - 1103.
- Chambers, Christopher P., 2005. "Allocation rules for land division," Journal of Economic Theory, Elsevier, vol. 121(2), pages 236-258, April.
- Nicolò, Antonio & Yu, Yan, 2008.
"Strategic divide and choose,"
Games and Economic Behavior,
Elsevier, vol. 64(1), pages 268-289, September.
- Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
- Z. Landau & O. Reid & I. Yershov, 2009. "A fair division solution to the problem of redistricting," Social Choice and Welfare, Springer, vol. 32(3), pages 479-492, March.
- Steven Brams & Michael Jones & Christian Klamler, 2008. "Proportional pie-cutting," International Journal of Game Theory, Springer, vol. 36(3), pages 353-367, March.
- Barbanel, Julius B. & Brams, Steven J., 2004. "Cake division with minimal cuts: envy-free procedures for three persons, four persons, and beyond," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 251-269, November.
- Francis Su, . "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Department of Economics).
If references are entirely missing, you can add them using this form.