Optimal Fair Division for Measures with Piecewise Linear Density Functions

Jerzy Legut ()
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Jerzy Legut: Department of Mathematics, Wrocław University of Technology, Wrocław, Poland

International Game Theory Review (IGTR), 2017, vol. 19, issue 02, 1-12

Abstract: A nonlinear programming method is used for finding an optimal fair division of the unit interval [0, 1) among n players. Preferences of players are described by nonatomic probability measures μ1,…,μn with piecewise linear (PWL) density functions. The presented algorithm can be applied for obtaining “almost†optimal fair divisions for measures with arbitrary density functions approximable by PWL functions. The number of cuts needed for obtaining such divisions is given.

Keywords: Fair division; cake cutting; optimal partitioning of a measurable space (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S0219198917500098

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