IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2610.08096.html

The lattice structure of the crawler

Author

Listed:
  • Hinata Kurashita

Abstract

We study object reallocation problems with single-peaked preferences. On the unrestricted domain of strict preferences, top trading cycles (TTC) is the unique rule that satisfies efficiency, individual rationality, and strategy-proofness. On the single-peaked preference domain, the crawler introduced by Bade (2019) satisfies the same properties. We show that the Nash equilibrium allocations of the crawler's direct revelation game form a complete lattice under weak Pareto dominance. The truthful allocation is the greatest element of this lattice, while the initial endowment allocation is its least element.

Suggested Citation

  • Hinata Kurashita, 2026. "The lattice structure of the crawler," Papers 2610.08096, arXiv.org.
    • Handle: RePEc:arx:papers:2610.08096
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2610.08096
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    2. Tamura, Yuki & Hosseini, Hadi, 2022. "The crawler: Three equivalence results for object (re)allocation problems when preferences are single-peaked," Journal of Economic Theory, Elsevier, vol. 203(C).
    3. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
    4. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    5. Bade, Sophie, 2019. "Matching with single-peaked preferences," Journal of Economic Theory, Elsevier, vol. 180(C), pages 81-99.
    6. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
    7. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
    8. Arribillaga, R. Pablo & Massó, Jordi & Neme, Alejandro, 2023. "All sequential allotment rules are obviously strategy-proof," Theoretical Economics, Econometric Society, vol. 18(3), July.
    9. Bochet, Olivier & Tumennasan, Norovsambuu, 2020. "Dominance of truthtelling and the lattice structure of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 185(C).
    10. Yuki Tamura, 2022. "Object reallocation problems under single-peaked preferences: two characterizations of the crawler," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 537-565, November.
    11. Shengwu Li, 2017. "Obviously Strategy-Proof Mechanisms," American Economic Review, American Economic Association, vol. 107(11), pages 3257-3287, November.
    Full references (including those not matched with items on IDEAS)

    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. Park, Changwoo, 2026. "Obviously strategy-proof implementation for mixed-ownership object-allocation problems," Journal of Mathematical Economics, Elsevier, vol. 124(C).
    2. Ishida, Wataru & Park, Changwoo, 2026. "Group incentive-compatible allocation of discrete resources when ownership is partitioned," Games and Economic Behavior, Elsevier, vol. 155(C), pages 287-309.
    3. Bochet, Olivier & Sakai, Toyotaka & Thomson, William, 2024. "Preference manipulations lead to the uniform rule," Journal of Economic Theory, Elsevier, vol. 220(C).
    4. Sumit Goel & Yuki Tamura, 2025. "TTC Domains," Papers 2501.15422, arXiv.org, revised Jun 2026.
    5. Morrill, Thayer & Roth, Alvin E., 2024. "Top trading cycles," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    6. Mackenzie, Andrew & Zhou, Yu, 2022. "Menu mechanisms," Journal of Economic Theory, Elsevier, vol. 204(C).
    7. Tamura, Yuki & Hosseini, Hadi, 2022. "The crawler: Three equivalence results for object (re)allocation problems when preferences are single-peaked," Journal of Economic Theory, Elsevier, vol. 203(C).
    8. Mackenzie, Andrew, 2020. "A revelation principle for obviously strategy-proof implementation," Games and Economic Behavior, Elsevier, vol. 124(C), pages 512-533.
    9. Tamura, Yuki, 2023. "Object reallocation problems with single-dipped preferences," Games and Economic Behavior, Elsevier, vol. 140(C), pages 181-196.
    10. Yannai A. Gonczarowski & Clayton Thomas, 2022. "Structural Complexities of Matching Mechanisms," Papers 2212.08709, arXiv.org, revised Mar 2024.
    11. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2006. "Changing the Boston School Choice Mechanism," Levine's Bibliography 122247000000001022, UCLA Department of Economics.
    12. Alexander L. Brown & Daniel G. Stephenson & Rodrigo A. Velez, 2024. "Testing the simplicity of strategy-proof mechanisms," Papers 2404.11883, arXiv.org.
    13. Di Feng, 2023. "Efficiency in Multiple-Type Housing Markets," Papers 2308.14989, arXiv.org, revised Feb 2025.
    14. Pycia, Marek & Unver, Utku, 2017. "Incentive compatible allocation and exchange of discrete resources," Theoretical Economics, Econometric Society, vol. 12(1), January.
    15. Louise Demoor & Mart'i Jan'e-Ballar'in & Pierre Nunn & Subhajit Pramanik & Antoine Pr'evotat & Makoto Yokoo, 2026. "Non-obvious Manipulability with Groups in Shapley-Scarf Housing Markets," Papers 2608.15631, arXiv.org.
    16. Yuki Tamura, 2022. "Object reallocation problems under single-peaked preferences: two characterizations of the crawler," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 537-565, November.
    17. Alexander L. Brown & Daniel G. Stephenson & Rodrigo A. Velez, 2026. "Testing the simplicity of strategy-proof mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 81(1), pages 13-42, February.
    18. James Schummer, 1999. "Almost-dominant Strategy Implementation," Discussion Papers 1278, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Yajing Chen & Zhenhua Jiao & Chenfeng Zhang & Luosai Zhang, 2021. "The Machiavellian frontier of top trading cycles," Papers 2106.14456, arXiv.org, revised Apr 2024.
    20. Takamiya, Koji, 2001. "Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 201-213, March.

    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:2610.08096. 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: https://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.