IDEAS home Printed from https://ideas.repec.org/a/spr/reecde/v23y2019i3d10.1007_s10058-019-00223-1.html
   My bibliography  Save this article

Notions of anonymity for object assignment: impossibility theorems

Author

Listed:
  • Hikaru Kondo

    (Osaka University)

Abstract

We search for impartiality in the allocation of objects when monetary transfers are not possible. Our main focus is anonymity. The standard definition requires that if agents’ names are permuted, their assignments be permuted in the same way. Since no rule satisfies this definition, we introduce weaker variants, “anonymity for distinct preferences,” “pairwise-anonymity for distinct preferences,” “pairwise-anonymity for fully differentiated profiles,” and “independence of others’ permutations.” We show that for more than two agents and two objects, no rule is pairwise-anonymous for distinct preferences and Pareto-efficient (Theorem 1), no rule is pairwise-anonymous for distinct preferences and independent of others’ permutations (Theorem 2), and no rule is pairwise-anonymous for fully differentiated profiles and strategy-proof (Theorem 3).

Suggested Citation

  • Hikaru Kondo, 2019. "Notions of anonymity for object assignment: impossibility theorems," Review of Economic Design, Springer;Society for Economic Design, vol. 23(3), pages 113-126, December.
    • Handle: RePEc:spr:reecde:v:23:y:2019:i:3:d:10.1007_s10058-019-00223-1
    DOI: 10.1007/s10058-019-00223-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10058-019-00223-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10058-019-00223-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 557-567.
    2. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    4. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
    5. John Hatfield, 2009. "Strategy-proof, efficient, and nonbossy quota allocations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 505-515, September.
    6. Takamiya, Koji, 2001. "Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 201-213, March.
    7. Onur Kesten & Ayşe Yazıcı, 2012. "The Pareto-dominant strategy-proof and fair rule for problems with indivisible goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 463-488, June.
    8. Anno, Hidekazu, 2015. "A short proof for the characterization of the core in housing markets," Economics Letters, Elsevier, vol. 126(C), pages 66-67.
    9. Miyagawa, Eiichi, 2002. "Strategy-Proofness and the Core in House Allocation Problems," Games and Economic Behavior, Elsevier, vol. 38(2), pages 347-361, February.
    10. Yoichi Kasajima, 2013. "Probabilistic assignment of indivisible goods with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 203-215, June.
    11. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
    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. Hikaru Kondo & Shigehiro Serizawa, 2015. "Notions of anonymity for object assignment: impossibility theorems," ISER Discussion Paper 0927, Institute of Social and Economic Research, Osaka University.
    2. Sonmez, Tayfun & Utku Unver, M., 2005. "House allocation with existing tenants: an equivalence," Games and Economic Behavior, Elsevier, vol. 52(1), pages 153-185, July.
    3. Yuji Fujinaka & Takuma Wakayama, 2011. "Secure implementation in Shapley–Scarf housing markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 147-169, September.
    4. Fujinaka, Yuji & Wakayama, Takuma, 2018. "Endowments-swapping-proof house allocation," Games and Economic Behavior, Elsevier, vol. 111(C), pages 187-202.
    5. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
    6. Marek Pycia & M. Utku Ünver, 2022. "Outside options in neutral allocation of discrete resources," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 581-604, December.
    7. Fujinaka, Yuji & Miyakawa, Toshiji, 2020. "Ex-post incentive compatible and individually rational assignments in housing markets with interdependent values," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 157-164.
    8. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    9. Kesten, Onur, 2009. "Why do popular mechanisms lack efficiency in random environments?," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2209-2226, September.
    10. Monte, Daniel & Tumennasan, Norovsambuu, 2015. "Centralized allocation in multiple markets," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 74-85.
    11. Kazuhiko Hashimoto, 2018. "Strategy-proofness and identical preferences lower bound in allocation problem of indivisible objects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 1045-1078, June.
    12. Liu, Peng & Zeng, Huaxia, 2019. "Random assignments on preference domains with a tier structure," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 176-194.
    13. Ehlers, Lars & Klaus, Bettina & Papai, Szilvia, 2002. "Strategy-proofness and population-monotonicity for house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 329-339, November.
    14. Morrill, Thayer & Roth, Alvin E., 2024. "Top trading cycles," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    15. Tayfun Sönmez & M. Utku Ünver, 2006. "Kidney Exchange with Good Samaritan Donors: A Characterization," Boston College Working Papers in Economics 640, Boston College Department of Economics.
    16. Pycia, Marek & Ãœnver, M. Utku, 2020. "Arrovian Efficiency and Auditability in the Allocation of Discrete Resources," CEPR Discussion Papers 15377, C.E.P.R. Discussion Papers.
    17. 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).
    18. Ehlers, Lars, 2014. "Top trading with fixed tie-breaking in markets with indivisible goods," Journal of Economic Theory, Elsevier, vol. 151(C), pages 64-87.
    19. Bogomolnaia, Anna & Deb, Rajat & Ehlers, Lars, 2005. "Strategy-proof assignment on the full preference domain," Journal of Economic Theory, Elsevier, vol. 123(2), pages 161-186, August.
    20. Pycia, Marek & Unver, Utku, 2017. "Incentive compatible allocation and exchange of discrete resources," Theoretical Economics, Econometric Society, vol. 12(1), January.

    More about this item

    Keywords

    Impartiality; Anonymity; Indivisible goods;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

    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:spr:reecde:v:23:y:2019:i:3:d:10.1007_s10058-019-00223-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.