IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2112.05632.html
   My bibliography  Save this paper

Truthful Cake Sharing

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2112.05632
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Haris Aziz & Alexander Lam & Barton E. Lee & Toby Walsh, 2021. "Strategyproof and Proportionally Fair Facility Location," Papers 2111.01566, arXiv.org, revised Nov 2023.
    4. Felix Brandt & Matthias Greger & Erel Segal-Halevi & Warut Suksompong, 2023. "Balanced Donor Coordination," Papers 2305.10286, arXiv.org.
    5. 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.
    6. Federico Echenique & Sumit Goel & SangMok Lee, 2022. "Stable allocations in discrete exchange economies," Papers 2202.04706, arXiv.org, revised Feb 2024.
    7. Xiaohui Bei & Guangda Huzhang & Warut Suksompong, 2018. "Truthful Fair Division without Free Disposal," Papers 1804.06923, arXiv.org, revised Apr 2020.
    8. Dinko Dimitrov & Ruud Hendrickx & Peter Borm, 2004. "Good and bad objects: the symmetric difference rule," Economics Bulletin, AccessEcon, vol. 4(11), pages 1-7.
    9. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2022. "Monotonicity in sharing the revenues from broadcasting sports leagues," European Journal of Operational Research, Elsevier, vol. 297(1), pages 338-346.
    10. Haris Aziz & Sujit Gujar & Manisha Padala & Mashbat Suzuki & Jeremy Vollen, 2022. "Coordinating Monetary Contributions in Participatory Budgeting," Papers 2206.05966, arXiv.org, revised Feb 2023.
    11. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    12. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2014. "Egalitarian equivalence and strategyproofness in the queueing problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 425-442, June.
    13. Efthymios Athanasiou & Juan D. Moreno-Ternero & Shlomo Weber, 2015. "Language learning and communicative benefits," Working Papers 15.09, Universidad Pablo de Olavide, Department of Economics.
    14. Tommy ANDERSSON & Lars EHLERS & Lars-Gunnar SVENSSON, 2014. "Transferring Ownership of Public Housing to Existing Tenants : A Mechanism Design Approach," Cahiers de recherche 09-2014, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    15. Karla Atkins & Achla Marathe & Chris Barrett, 2007. "A computational approach to modeling commodity markets," Computational Economics, Springer;Society for Computational Economics, vol. 30(2), pages 125-142, September.
    16. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    17. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2014. "Assigning agents to a line," Games and Economic Behavior, Elsevier, vol. 87(C), pages 539-553.
    18. Erel Segal-Halevi, 2019. "Fair Division with Bounded Sharing," Papers 1912.00459, arXiv.org.
    19. Hervé Moulin & Jay Sethuraman, 2013. "The Bipartite Rationing Problem," Operations Research, INFORMS, vol. 61(5), pages 1087-1100, October.
    20. Andersson, Tommy & Csehz, Ágnes & Ehlers, Lars & Erlanson, Albin, 2018. "Organizing Time Banks: Lessons from Matching Markets," Working Papers 2018:19, Lund University, Department of Economics, revised 08 Mar 2019.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2112.05632. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.