Elementary Solution to the Fair Division Problem
Pages 53 - 70
Abstract
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 properties of 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.
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© Pleiades Publishing, Inc. 2024.
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Plenum Press
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Publication History
Published: 07 August 2024
Accepted: 23 May 2024
Revision received: 23 May 2024
Received: 18 January 2024
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