Elementary solution to the fair division problem

Fuente: arXiv
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Main Authors: Blank, Michael, Polyakov, Maxim
Format: Preprint
Published: 2024
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author Blank, Michael
Polyakov, Maxim
author_facet Blank, Michael
Polyakov, Maxim
contents A new and relatively elementary approach is proposed for solving the problem of fair division of a continuous resource (measurable space, pie, etc.) between several participants, the selection criteria of which are described by charges (signed measures). The setting of the problem with charges is considered for the first time. The problem comes down to analyzing the properties of the trajectories of a specially constructed dynamical system acting in the space of finite measurable partitions. Exponentially fast convergence to a limit solution is proved for both the case of true measures and the case of charges.
format Preprint
id arxiv_https___arxiv_org_abs_2406_00733
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Elementary solution to the fair division problem
Blank, Michael
Polyakov, Maxim
Dynamical Systems
Optimization and Control
91B32
A new and relatively elementary approach is proposed for solving the problem of fair division of a continuous resource (measurable space, pie, etc.) between several participants, the selection criteria of which are described by charges (signed measures). The setting of the problem with charges is considered for the first time. The problem comes down to analyzing the properties of the trajectories of a specially constructed dynamical system acting in the space of finite measurable partitions. Exponentially fast convergence to a limit solution is proved for both the case of true measures and the case of charges.
title Elementary solution to the fair division problem
topic Dynamical Systems
Optimization and Control
91B32
url https://arxiv.org/abs/2406.00733