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Truthful Cake Sharing

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  • Xiaohui Bei
  • Xinhang Lu
  • Warut Suksompong

Abstract

The classic cake cutting problem concerns the fair allocation of a heterogeneous resource among interested agents. In this paper, we study a public goods variant of the problem, where instead of competing with one another for the cake, the agents all share the same subset of the cake which must be chosen subject to a length constraint. We focus on the design of truthful and fair mechanisms in the presence of strategic agents who have piecewise uniform utilities over the cake. On the one hand, we show that the leximin solution is truthful and moreover maximizes an egalitarian welfare measure among all truthful and position oblivious mechanisms. On the other hand, we demonstrate that the maximum Nash welfare solution is truthful for two agents but not in general. Our results assume that mechanisms can block each agent from accessing parts that the agent does not claim to desire; we provide an impossibility result when blocking is not allowed.

Suggested Citation

  • Xiaohui Bei & Xinhang Lu & Warut Suksompong, 2021. "Truthful Cake Sharing," Papers 2112.05632, arXiv.org, revised Feb 2022.
    • Handle: RePEc:arx:papers:2112.05632
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    References listed on IDEAS

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    1. Xiaohui Bei & Guangda Huzhang & Warut Suksompong, 2018. "Truthful Fair Division without Free Disposal," Papers 1804.06923, arXiv.org, revised Apr 2020.
    2. Haris Aziz & Anna Bogomolnaia & Hervé Moulin, 2019. "Fair Mixing: the Case of Dichotomous Preferences," Post-Print hal-03047451, HAL.
    3. 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.
    4. 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.
    5. Erel Segal-Halevi & Balázs R. Sziklai, 2019. "Monotonicity and competitive equilibrium in cake-cutting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 363-401, September.
    6. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, January.
    7. Brandl, Florian & Brandt, Felix & Greger, Matthias & Peters, Dominik & Stricker, Christian & Suksompong, Warut, 2022. "Funding public projects: A case for the Nash product rule," Journal of Mathematical Economics, Elsevier, vol. 99(C).
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    Cited by:

    1. Suksompong, Warut, 2023. "A characterization of maximum Nash welfare for indivisible goods," Economics Letters, Elsevier, vol. 222(C).
    2. Warut Suksompong, 2022. "A Characterization of Maximum Nash Welfare for Indivisible Goods," Papers 2212.04203, arXiv.org, revised Dec 2022.

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