IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2204.08300.html
   My bibliography  Save this paper

Axiomatic Characterizations of Draft Rules

Author

Listed:
  • Jacob Coreno
  • Ivan Balbuzanov

Abstract

Drafts are sequential allocation procedures for distributing heterogeneous and indivisible objects among agents subject to some priority order (e.g., allocating players' contract rights to teams in professional sports leagues). Agents report ordinal preferences over objects and bundles are partially ordered by pairwise comparison. We provide a simple characterization of draft rules: they are the only allocation rules which are respectful of a priority (RP), envy-free up to one object (EF1), non-wasteful (NW) and resource monotonic (RM). RP and EF1 are crucial for competitive balance in sports leagues. We also prove three related impossibility theorems showing that the competitive-balance axioms RP and EF1 are generally incompatible with strategy-proofness. However, draft rules satisfy maxmin strategy-proofness. If agents may declare some objects unacceptable, then draft rules are characterized by RP, EF1, NW, and RM, in conjunction with individual rationality and truncation invariance. In a model with variable populations, draft rules are characterized by EF1, EFF, and RM, together with (population) consistency, top-object consistency, and neutrality.

Suggested Citation

  • Jacob Coreno & Ivan Balbuzanov, 2022. "Axiomatic Characterizations of Draft Rules," Papers 2204.08300, arXiv.org, revised May 2024.
  • Handle: RePEc:arx:papers:2204.08300
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2204.08300
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 265-280, October.
    2. Szilvia Pápai, 2001. "Strategyproof and Nonbossy Multiple Assignments," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(3), pages 257-271, July.
    3. Lars Ehlers & Bettina Klaus, 2014. "Strategy-Proofness Makes the Difference: Deferred-Acceptance with Responsive Priorities," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 949-966, November.
    4. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Unver, Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    5. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    6. 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.
    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. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    2. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    3. Afacan, Mustafa Oğuz & Bó, Inácio, 2022. "Strategy-proof popular mechanisms," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    4. Sean Horan & Vikram Manjunath, 2022. "Lexicographic Composition of Choice Functions," Papers 2209.09293, arXiv.org.
    5. Monte, Daniel & Tumennasan, Norovsambuu, 2015. "Centralized allocation in multiple markets," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 74-85.
    6. Eric Budish & Judd B. Kessler, 2022. "Can Market Participants Report Their Preferences Accurately (Enough)?," Management Science, INFORMS, vol. 68(2), pages 1107-1130, February.
    7. Nhan-Tam Nguyen & Dorothea Baumeister & Jörg Rothe, 2018. "Strategy-proofness of scoring allocation correspondences for indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 101-122, January.
    8. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    9. Biró, Péter & Klijn, Flip & Pápai, Szilvia, 2022. "Serial Rules in a Multi-Unit Shapley-Scarf Market," Games and Economic Behavior, Elsevier, vol. 136(C), pages 428-453.
    10. Monte, Daniel & Tumennasan, Norovsambuu, 2013. "Matching with quorums," Economics Letters, Elsevier, vol. 120(1), pages 14-17.
    11. Hoda Atef Yekta & Robert Day, 2020. "Optimization-based Mechanisms for the Course Allocation Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 641-660, July.
    12. Honda, Edward, 2021. "A modified deferred acceptance algorithm for conditionally lexicographic-substitutable preferences," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    13. Bettina Klaus & Alexandru Nichifor, 2020. "Serial dictatorship mechanisms with reservation prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 665-684, October.
    14. 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.
    15. Franz Diebold & Haris Aziz & Martin Bichler & Florian Matthes & Alexander Schneider, 2014. "Course Allocation via Stable Matching," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 6(2), pages 97-110, April.
    16. Jörgen Kratz, 2017. "Overlapping multiple object assignments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 723-753, March.
    17. Gian Caspari, 2023. "A market design solution to a multi-category housing allocation problem," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 8(1), pages 75-96, December.
    18. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    19. Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.
    20. Markus Möller, 2024. "Transparent Matching Mechanisms," ECONtribute Discussion Papers Series 306, University of Bonn and University of Cologne, Germany.

    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:2204.08300. 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.