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Mark-Choose-Cut Algorithms For Fair And Strongly Fair Division

Author

Listed:
  • Harunor Shishido

    (Kagawa University, cKagawa)

  • Dao-Zhi Zeng

    (Kagawa University, cKagawa)

Abstract

This paper proposes a new criterion to evaluate algorithms for cake division, by the number of resulting pieces. Then, inspired by the idea of "cut-and-choose", we present "mark-choose-cut" algorithms for fair and strongly fair cake division problems. They are game-theoretic algorithms. The number of resulting pieces is bounded by 2 × 3n-2 + 1 and 4 × 3n-2 + 1, for fair and strongly fair division respectively.

Suggested Citation

  • Harunor Shishido & Dao-Zhi Zeng, 1999. "Mark-Choose-Cut Algorithms For Fair And Strongly Fair Division," Group Decision and Negotiation, Springer, vol. 8(2), pages 125-137, March.
    • Handle: RePEc:spr:grdene:v:8:y:1999:i:2:d:10.1023_a:1008620404353
    DOI: 10.1023/A:1008620404353
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    Citations

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    Cited by:

    1. Fedor Sandomirskiy & Erel Segal-Halevi, 2019. "Efficient Fair Division with Minimal Sharing," Papers 1908.01669, arXiv.org, revised Apr 2022.
    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.
    3. SEGAL-HALEVI, Erel & NITZAN, Shmuel, 2018. "Fair Cake-Cutting among Families," Discussion paper series HIAS-E-79, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    4. Erel Segal-Halevi & Shmuel Nitzan, 2019. "Fair cake-cutting among families," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 709-740, December.
    5. Agnes Cseh & Tamás Fleiner, 2018. "The complexity of cake cutting with unequal shares," CERS-IE WORKING PAPERS 1819, Institute of Economics, Centre for Economic and Regional Studies.

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