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3 Persons, 2 Cuts: A Maximin Envy-Free and a Maximally Equitable Cake-Cutting Algorithm

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  • Brams, Steven
  • Landweber, Peter

Abstract

We describe a 3-person, 2-cut envy-free cake-cutting algorithm, inspired by a continuous moving-knife procedure, that does not require that the players continuously move knifes across the cake. By having the players submit their value functions over the cake to a referee—rather than move knives according to these functions—the referee can ensure that the division is not only envy-free but also maximin. In addition, the referee can use the value functions to find a maximally equitable division, whereby the players receive equally valued shares that are maximal, but this allocation may not be envy-free.

Suggested Citation

  • Brams, Steven & Landweber, Peter, 2018. "3 Persons, 2 Cuts: A Maximin Envy-Free and a Maximally Equitable Cake-Cutting Algorithm," MPRA Paper 84683, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:84683
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    File URL: https://mpra.ub.uni-muenchen.de/84683/1/MPRA_paper_84683.pdf
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    References listed on IDEAS

    as
    1. Barbanel,Julius B. Introduction by-Name:Taylor,Alan D., 2005. "The Geometry of Efficient Fair Division," Cambridge Books, Cambridge University Press, number 9780521842488.
    2. Barbanel, Julius B. & Brams, Steven J., 2004. "Cake division with minimal cuts: envy-free procedures for three persons, four persons, and beyond," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 251-269, November.
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    More about this item

    Keywords

    Fair division; cake-cutting; envy-freeness; equitability;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

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