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Obvious manipulations in cake-cutting

Author

Listed:
  • Ortega, Josué
  • Segal-Halevi, Erel
Abstract
In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n = 2 it implies a dictatorial allocation, whereas for n Ï 3 it requires that one agent receives no cake. We show that a weaker version of this property recently suggested by Troyan and Morril, called not-obvious manipulability, is compatible with the strong fairness property of proportionality, which guarantees that each agent receives 1/n of the cake. Both properties are satisfied by the leftmost leaves mechanism, an adaptation of the Dubins - Spanier moving knife procedure. Most other classical proportional mechanisms in literature are obviously manipulable, including the original moving knife mechanism. Not-obvious manipulability explains why leftmost leaves is manipulated less often in practice than other proportional mechanisms.

Suggested Citation

  • Ortega, Josué & Segal-Halevi, Erel, 2019. "Obvious manipulations in cake-cutting," ZEW Discussion Papers 19-056, ZEW - Leibniz Centre for European Economic Research.
    • Handle: RePEc:zbw:zewdip:19056
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    References listed on IDEAS

    as
    1. Kyropoulou, Maria & Ortega, Josué & Segal-Halevi, Erel, 2022. "Fair cake-cutting in practice," Games and Economic Behavior, Elsevier, vol. 133(C), pages 28-49.
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    6. Segal-Halevi, Erel & Nitzan, Shmuel & Hassidim, Avinatan & Aumann, Yonatan, 2017. "Fair and square: Cake-cutting in two dimensions," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 1-28.
    7. Nicolò, Antonio & Yu, Yan, 2008. "Strategic divide and choose," Games and Economic Behavior, Elsevier, vol. 64(1), pages 268-289, September.
    8. Segal-Halevi, Erel & Sziklai, Balázs R., 2018. "Resource-monotonicity and population-monotonicity in connected cake-cutting," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 19-30.
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    11. Parag A. Pathak & Tayfun Sönmez, 2013. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," American Economic Review, American Economic Association, vol. 103(1), pages 80-106, February.
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    13. 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.
    14. Schummer, James, 2004. "Almost-dominant strategy implementation: exchange economies," Games and Economic Behavior, Elsevier, vol. 48(1), pages 154-170, July.
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    Cited by:

    1. Haris Aziz & Alexander Lam, 2021. "Obvious Manipulability of Voting Rules," Papers 2111.01983, arXiv.org, revised Jun 2022.
    2. Bhardwaj, Bhavook & Kumar, Rajnish & Ortega, Josué, 2020. "Fairness and efficiency in cake-cutting with single-peaked preferences," Economics Letters, Elsevier, vol. 190(C).
    3. Arribillaga, R. Pablo & Bonifacio, Agustín G., 2024. "Obvious manipulations of tops-only voting rules," Games and Economic Behavior, Elsevier, vol. 143(C), pages 12-24.
    4. Kyropoulou, Maria & Ortega, Josué & Segal-Halevi, Erel, 2022. "Fair cake-cutting in practice," Games and Economic Behavior, Elsevier, vol. 133(C), pages 28-49.
    5. SHINOZAKI, Hiroki, 2023. "Non-obvious manipulability and efficiency in package assignment problems with money for agents with income effects and hard budget constraints," Discussion paper series HIAS-E-136, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    6. Pablo R. Arribillaga & Eliana Pepa Risma, 2023. "Obvious Manipulations in Matching with and without Contracts," Working Papers 257, Red Nacional de Investigadores en Economía (RedNIE).

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    More about this item

    Keywords

    cake-cutting; not-obvious manipulability; prior-free mechanism design;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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