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How to obtain an equitable optimal fair division

Author

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  • Jerzy Legut

    (Wrocław University of Science and Technology)

Abstract

A nonlinear programming method is used for finding an equitable optimal fair division of the unit interval [0, 1) among n players. Players’ preferences are described by nonatomic probability measures $$\mu _{1},\ldots ,\mu _{n}$$μ1,…,μn with density functions having piecewise strict monotone likelihood ratio property. The presented algorithm can be used to obtain also an equitable $$\varepsilon $$ε-optimal fair division in case of measures with arbitrary differentiable density functions. An example of an equitable optimal fair division for three players is given.

Suggested Citation

  • Jerzy Legut, 2020. "How to obtain an equitable optimal fair division," Annals of Operations Research, Springer, vol. 284(1), pages 323-332, January.
    • Handle: RePEc:spr:annopr:v:284:y:2020:i:1:d:10.1007_s10479-018-3053-2
    DOI: 10.1007/s10479-018-3053-2
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    References listed on IDEAS

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    1. Marco Dall’Aglio & Camilla Luca, 2014. "Finding maxmin allocations in cooperative and competitive fair division," Annals of Operations Research, Springer, vol. 223(1), pages 121-136, December.
    2. 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.
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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.

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