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Optimal Fair Division for Measures with Piecewise Linear Density Functions

Author

Listed:
  • Jerzy Legut

    (Department of Mathematics, Wrocław University of Technology, Wrocław, Poland)

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.

Suggested Citation

  • Jerzy Legut, 2017. "Optimal Fair Division for Measures with Piecewise Linear Density Functions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-12, June.
    • Handle: RePEc:wsi:igtrxx:v:19:y:2017:i:02:n:s0219198917500098
    DOI: 10.1142/S0219198917500098
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    Cited by:

    1. Yuan Gao & Christian Kroer, 2020. "Infinite-Dimensional Fisher Markets and Tractable Fair Division," Papers 2010.03025, arXiv.org, revised Apr 2021.
    2. Jerzy Legut, 2020. "How to obtain an equitable optimal fair division," Annals of Operations Research, Springer, vol. 284(1), pages 323-332, January.
    3. Legut, Jerzy, 2020. "Simple fair division of a square," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 35-40.

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