Cake Cutting – Fair and Square
Erel Segal-Halevi and
Shmuel Nitzan ()
No 2014-01, Working Papers from Bar-Ilan University, Department of Economics
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.
Keywords: fair division; cake cutting; land division; geometry; non-additive utilities; social welfare (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed
Downloads: (external link)
http://econ.biu.ac.il/files/economics/working-papers/2014-01.pdf Working paper (application/pdf)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:biu:wpaper:2014-01
Access Statistics for this paper
More papers in Working Papers from Bar-Ilan University, Department of Economics Contact information at EDIRC.
Series data maintained by Department of Economics ().