IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v4y2013i1p21-37d22968.html
   My bibliography  Save this article

An Equilibrium Analysis of Knaster’s Fair Division Procedure

Author

Listed:
  • Matt Van Essen

    (Department of Economics, Finance, and Legal Studies, University of Alabama, Tuscaloosa, AL 35487, USA)

Abstract

In an incomplete information setting, we analyze the sealed bid auction proposed by Knaster (cf. Steinhaus (1948)). This procedure was designed to efficiently and fairly allocate multiple indivisible items when participants report their valuations truthfully. In equilibrium, players do not follow truthful bidding strategies. We find that, ex-post, the equilibrium allocation is still efficient but may not be fair. However, on average, participants receive the same outcome they would have received if everyone had reported truthfully— i.e. , the mechanism is ex-ante fair.

Suggested Citation

  • Matt Van Essen, 2013. "An Equilibrium Analysis of Knaster’s Fair Division Procedure," Games, MDPI, vol. 4(1), pages 1-17, January.
    • Handle: RePEc:gam:jgames:v:4:y:2013:i:1:p:21-37:d:22968
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/4/1/21/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/4/1/21/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Preston McAfee, R., 1992. "Amicable divorce: Dissolving a partnership with simple mechanisms," Journal of Economic Theory, Elsevier, vol. 56(2), pages 266-293, April.
    2. Crawford, V. P. & Heller, W. P., 1979. "Fair division with indivisible commodities," Journal of Economic Theory, Elsevier, vol. 21(1), pages 10-27, August.
    3. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
    4. Tadenuma, Koichi & Thomson, William, 1993. "The fair allocation of an indivisible good when monetary compensations are possible," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 117-132, February.
    5. Benny Moldovanu, 2002. "How to Dissolve a Partnership," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 158(1), pages 66-80, March.
    6. Vincent P. Crawford, 1977. "A Game of Fair Division," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 235-247.
    7. Vincent P. Crawford, 1980. "A Self-administered Solution of the Bargaining Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(2), pages 385-392.
    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. Brown, Alexander L. & Van Essen, Matt, 2022. "Breaking-up should not be hard to do! Designing contracts to avoid wars of attrition," European Economic Review, Elsevier, vol. 143(C).

    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. Nicolò, Antonio & Velez, Rodrigo A., 2017. "Divide and compromise," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 100-110.
    2. Richard R. W. Brooks & Claudia M. Landeo & Kathryn E. Spier, 2010. "Trigger happy or gun shy? Dissolving common‐value partnerships with Texas shootouts," RAND Journal of Economics, RAND Corporation, vol. 41(4), pages 649-673, December.
    3. Brown, Alexander L. & Velez, Rodrigo A., 2016. "The costs and benefits of symmetry in common-ownership allocation problems," Games and Economic Behavior, Elsevier, vol. 96(C), pages 115-131.
    4. Van Essen, Matt & Wooders, John, 2016. "Dissolving a partnership dynamically," Journal of Economic Theory, Elsevier, vol. 166(C), pages 212-241.
    5. R?bert F. Veszteg, 2004. "Fairness under Uncertainty with Indivisibilities," UFAE and IAE Working Papers 613.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    6. Nicolò, Antonio & Yu, Yan, 2008. "Strategic divide and choose," Games and Economic Behavior, Elsevier, vol. 64(1), pages 268-289, September.
    7. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    8. Bossert, Walter, 1998. "Welfarism and rationalizability in allocation problems with indivisibilities1," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 133-150, March.
    9. 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.
    10. Kranich, Laurence, 1995. "Equity and economic theory: reflections on methodology and scope," UC3M Working papers. Economics 3919, Universidad Carlos III de Madrid. Departamento de Economía.
    11. Tommy ANDERSSON & Lars EHLERS, 2013. "An Algorithm for Identifying Agent-k-Linked Allocations in Economies with Indivisibilities," Cahiers de recherche 17-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    12. Ornelas, Emanuel & Turner, John L., 2007. "Efficient dissolution of partnerships and the structure of control," Games and Economic Behavior, Elsevier, vol. 60(1), pages 187-199, July.
    13. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
    14. Nicola Dimitri, 2021. "The “Italian Football Federation Auction” for Co-ownership Resolution," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 58(2), pages 275-285, March.
    15. María‐Angeles de Frutos & Thomas Kittsteiner, 2008. "Efficient partnership dissolution under buy‐sell clauses," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 184-198, March.
    16. Zhan Wang & Jinpeng Ma & Hongwei Zhang, 2023. "Object-based unawareness: Theory and applications," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 8(1), pages 1-55, December.
    17. Toyotaka Sakai, 2008. "Second price auctions on general preference domains: two characterizations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(2), pages 347-356, November.
    18. Sakai, Toyotaka, 2007. "Fairness and implementability in allocation of indivisible objects with monetary compensations," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 549-563, June.
    19. Velez, Rodrigo A., 2023. "Equitable rent division on a soft budget," Games and Economic Behavior, Elsevier, vol. 139(C), pages 1-14.
    20. , & , & ,, 2014. "Budget-balance, fairness and minimal manipulability," Theoretical Economics, Econometric Society, vol. 9(3), September.

    More about this item

    Keywords

    fair division; auction;

    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:gam:jgames:v:4:y:2013:i:1:p:21-37:d:22968. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.