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N-Person cake-cutting: there may be no perfect division

Steven Brams, Michael A. Jones and Christian Klamler

MPRA Paper from University Library of Munich, Germany

Abstract: A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envy-free, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by a 3-cut and a 4-cut division, which raises the question of whether the 3-cut division, which is not efficient, or the 4-cut division, which is not envy-free, is more desirable (a 2-cut division can at best satisfy either envy-freeness or equitability but not both). We prove that no perfect division exists for an extension of the example for three or more players.

Keywords: Cake-cutting; fair division; efficiency; envy-freeness; equitability; heterogeneous good (search for similar items in EconPapers)
JEL-codes: C61 C72 D30 D61 D63 D71 D74 (search for similar items in EconPapers)
Date: 2011-10-22
New Economics Papers: this item is included in nep-cis, nep-gth, nep-hpe and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6) Track citations by RSS feed

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