Cake Cutting – Fair and Square
The 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.
|Date of creation:||Jan 2014|
|Date of revision:|
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- Nicolò, Antonio & Yu, Yan, 2008.
"Strategic divide and choose,"
Games and Economic Behavior,
Elsevier, vol. 64(1), pages 268-289, September.
- Dall'Aglio, Marco & Maccheroni, Fabio, 2009.
Games and Economic Behavior,
Elsevier, vol. 66(1), pages 57-77, May.
- 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;The Society for Social Choice and Welfare, 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.
- 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.
- Steven Brams & Michael Jones & Christian Klamler, 2008. "Proportional pie-cutting," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 353-367, March.
- 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).
- 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.
- 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;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 27-45, July.
- Marco LiCalzi & Antonio Nicolò, 2005. "Efficient Egalitarian Equivalent Allocations over a Single Good," Microeconomics 0510014, EconWPA.
- Z. Landau & O. Reid & I. Yershov, 2009. "A fair division solution to the problem of redistricting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 479-492, March.
- William Thomson, 2007. "Children Crying at Birthday Parties. Why?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 501-521, June.
- Chambers, Christopher P., 2005. "Allocation rules for land division," Journal of Economic Theory, Elsevier, vol. 121(2), pages 236-258, April.
- 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.
- Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
- 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.
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