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Truth, justice, and cake cutting

Author

Listed:
  • Chen, Yiling
  • Lai, John K.
  • Parkes, David C.
  • Procaccia, Ariel D.

Abstract

Cake cutting is a common metaphor for the division of a heterogeneous divisible good. There are numerous papers that study the problem of fairly dividing a cake; a small number of them also take into account self-interested agents and consequent strategic issues, but these papers focus on fairness and consider a strikingly weak notion of truthfulness. In this paper we investigate the problem of cutting a cake in a way that is truthful, Pareto-efficient, and fair, where for the first time our notion of dominant strategy truthfulness is the ubiquitous one in social choice and computer science. We design both deterministic and randomized cake cutting mechanisms that are truthful and fair under different assumptions with respect to the valuation functions of the agents.

Suggested Citation

  • Chen, Yiling & Lai, John K. & Parkes, David C. & Procaccia, Ariel D., 2013. "Truth, justice, and cake cutting," Games and Economic Behavior, Elsevier, vol. 77(1), pages 284-297.
    • Handle: RePEc:eee:gamebe:v:77:y:2013:i:1:p:284-297
    DOI: 10.1016/j.geb.2012.10.009
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Josué Ortega & Erel Segal-Halevi, 2022. "Obvious manipulations in cake-cutting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 969-988, November.
    2. 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.
    3. Erel Segal-Halevi & Shmuel Nitzan & Avinatan Hassidim & Yonatan Aumann, 2020. "Envy-Free Division of Land," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 896-922, August.
    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. Xiaohui Bei & Xinhang Lu & Warut Suksompong, 2021. "Truthful Cake Sharing," Papers 2112.05632, arXiv.org, revised Feb 2022.
    6. Yuan Gao & Christian Kroer, 2020. "Infinite-Dimensional Fisher Markets and Tractable Fair Division," Papers 2010.03025, arXiv.org, revised Apr 2021.
    7. Simina Br^anzei & MohammadTaghi Hajiaghayi & Reed Phillips & Suho Shin & Kun Wang, 2024. "Dueling Over Dessert, Mastering the Art of Repeated Cake Cutting," Papers 2402.08547, arXiv.org, revised Feb 2024.
    8. Matt Essen & John Wooders, 2020. "Dissolving a partnership securely," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 415-434, March.
    9. Fedor Sandomirskiy & Erel Segal-Halevi, 2019. "Efficient Fair Division with Minimal Sharing," Papers 1908.01669, arXiv.org, revised Apr 2022.
    10. Samuel Bismuth & Ivan Bliznets & Erel Segal-Halevi, 2019. "Fair Division with Bounded Sharing: Binary and Non-Degenerate Valuations," Papers 1912.00459, arXiv.org, revised Jul 2024.
    11. Erel Segal-Halevi & Shmuel Nitzan, 2014. "Cake Cutting – Fair and Square," Working Papers 2014-01, Bar-Ilan University, Department of Economics.
    12. Xiaohui Bei & Guangda Huzhang & Warut Suksompong, 2020. "Truthful fair division without free disposal," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(3), pages 523-545, October.
    13. Mackenzie, Andrew & Komornik, Vilmos, 2023. "Fairly taking turns," Games and Economic Behavior, Elsevier, vol. 142(C), pages 743-764.
    14. Maria Kyropoulou & Josu'e Ortega & Erel Segal-Halevi, 2018. "Fair Cake-Cutting in Practice," Papers 1810.08243, arXiv.org, revised Feb 2022.
    15. Ji-Won Park & Jaeup U. Kim & Cheol-Min Ghim & Chae Un Kim, 2021. "The Boltzmann fair division for distributive justice," Papers 2109.11917, arXiv.org, revised Nov 2021.
    16. Van Essen, Matt & Wooders, John, 2016. "Dissolving a partnership dynamically," Journal of Economic Theory, Elsevier, vol. 166(C), pages 212-241.
    17. Chèze, Guillaume, 2019. "Cake cutting: Explicit examples for impossibility results," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 68-72.
    18. Cubukcu, K. Mert, 2020. "The problem of fair division of surplus development rights in redevelopment of urban areas: Can the Shapley value help?," Land Use Policy, Elsevier, vol. 91(C).
    19. Tarbush, Bassel, 2018. "Hotelling competition and the gamma distribution," Games and Economic Behavior, Elsevier, vol. 111(C), pages 222-240.
    20. Hoang, Lê Nguyên & Soumis, François & Zaccour, Georges, 2016. "Measuring unfairness feeling in allocation problems," Omega, Elsevier, vol. 65(C), pages 138-147.

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    More about this item

    Keywords

    Fair division; Envy-freeness; Cake cutting; Maximum flows; Strategy-proofness; Mechanism design;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • 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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