Simple fair division of a square

Jerzy Legut

Journal of Mathematical Economics, 2020, vol. 86, issue C, 35-40

Abstract: Suppose we are given a cake represented by the unit interval to be divided among agents evaluating the pieces of the cake by nonatomic probability measures. It is known that we can divide the unit interval into contiguous and connected pieces and assign them to the agents in such a way that the values of the pieces are equal according to the individual agents measures. Such division is said to be equitable and simple. In this paper we show that an equitable and simple division also exists in the case of dividing two-dimensional cake represented by the unit square. In this case, by simple division we mean dividing the unit square firstly by horizontal cuts, and then partition the resulting rectangles by vertical cuts. We give a method of obtaining a proportional and simple division of this cake. Furthermore, we prove the existence of proportional, equitable and simple division.

Keywords: Equitable division; Land division; Cake-cutting (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304406819301090
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:86:y:2020:i:c:p:35-40

DOI: 10.1016/j.jmateco.2019.11.001

Access Statistics for this article

Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii

More articles in Journal of Mathematical Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().