IDEAS home Printed from https://ideas.repec.org/p/yor/yorken/19-12.html
   My bibliography  Save this paper

A Conic Approach to the Implementation of Reduced-Form Allocation Rules

Author

Listed:
  • Xu Lang
  • Zaifu Yang

Abstract

We examine the implementation of reduced-form allocation rules in mechanism design problems. To handle the problem, we adopt a conic approach which uses a lift-and-project method to construct a projection cone and find its finite generators. This results in a set of implementable reduced forms for implementation. We then characterize projection cones for several typical mechanism design problems including single-item auctions, bilateral trade, compromise, and multiple-item auctions with group capacity constraints. We find that the implementation condition in general has a linear characterization by a class of sign functions, which is larger and richer than the well-known class of characteristic functions found by Border. These results admit meaningful economic interpretations.

Suggested Citation

  • Xu Lang & Zaifu Yang, 2019. "A Conic Approach to the Implementation of Reduced-Form Allocation Rules," Discussion Papers 19/12, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:19/12
    as

    Download full text from publisher

    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2019/1912.pdf
    File Function: Main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Börgers, Tilman & Postl, Peter, 2009. "Efficient compromising," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2057-2076, September.
    2. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-1187, July.
    3. Kim Border, 2007. "Reduced Form Auctions Revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 167-181, April.
    4. Che, Yeon-Koo & Condorelli, Daniele & Kim, Jinwoo, 2018. "Weak cartels and collusion-proof auctions," Journal of Economic Theory, Elsevier, vol. 178(C), pages 398-435.
    5. Yeon‐Koo Che & Jinwoo Kim & Konrad Mierendorff, 2013. "Generalized Reduced‐Form Auctions: A Network‐Flow Approach," Econometrica, Econometric Society, vol. 81(6), pages 2487-2520, November.
    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. Xu Lang, 2022. "Reduced-Form Allocations with Complementarity: A 2-Person Case," Papers 2202.06245, arXiv.org, revised Feb 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. Xu Lang & Zaifu Yang, 2023. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 23/02, Department of Economics, University of York.
    2. Xu Lang, 2022. "Reduced-Form Allocations with Complementarity: A 2-Person Case," Papers 2202.06245, arXiv.org, revised Feb 2022.
    3. Goeree, Jacob K. & Kushnir, Alexey, 2016. "Reduced form implementation for environments with value interdependencies," Games and Economic Behavior, Elsevier, vol. 99(C), pages 250-256.
    4. Sergiu Hart & Philip J. Reny, 2015. "Implementation of reduced form mechanisms: a simple approach and a new characterization," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 1-8, April.
    5. Tim Roughgarden, 2018. "Complexity Theory, Game Theory, and Economics: The Barbados Lectures," Papers 1801.00734, arXiv.org, revised Feb 2020.
    6. Xu Lang & Zaifu Yang, 2021. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints: A Revision," Discussion Papers 21/05, Department of Economics, University of York.
    7. Saeed Alaei & Hu Fu & Nima Haghpanah & Jason Hartline & Azarakhsh Malekian, 2019. "Efficient Computation of Optimal Auctions via Reduced Forms," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1058-1086, August.
    8. Xu Lang, 2023. "A Belief-Based Characterization of Reduced-Form Auctions," Papers 2307.04070, arXiv.org.
    9. Erya Yang, 2021. "Reduced-form mechanism design and ex post fairness constraints," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 269-293, October.
    10. Xu Lang, 2022. "Reduced-form budget allocation with multiple public alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 335-359, August.
    11. Xu Lang & Zaifu Yang, 2021. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 21/04, Department of Economics, University of York.
    12. Mierendorff, Konrad, 2011. "Asymmetric reduced form Auctions," Economics Letters, Elsevier, vol. 110(1), pages 41-44, January.
    13. Xu Lang & Debasis Mishra, 2022. "Symmetric reduced form voting," Papers 2207.09253, arXiv.org, revised Apr 2023.
    14. Li, Yunan, 2019. "Efficient mechanisms with information acquisition," Journal of Economic Theory, Elsevier, vol. 182(C), pages 279-328.
    15. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2021. "A Theory of Auctions with Endogenous Valuations," Journal of Political Economy, University of Chicago Press, vol. 129(4), pages 1011-1051.
    16. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Strategy-proof multi-object auction design: Ex-post revenue maximization with no wastage," ISER Discussion Paper 1001, Institute of Social and Economic Research, Osaka University.
    17. Yingkai Li & Xiaoyun Qiu, 2023. "Screening Signal-Manipulating Agents via Contests," Papers 2302.09168, arXiv.org, revised Feb 2024.
    18. Pai, Mallesh M. & Vohra, Rakesh, 2014. "Optimal auctions with financially constrained buyers," Journal of Economic Theory, Elsevier, vol. 150(C), pages 383-425.
    19. Yunan Li, 2017. "Efficient Mechanisms with Information Acquisition," PIER Working Paper Archive 16-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 23 Jun 2017.
    20. Lang, Xu & Mishra, Debasis, 0. "Symmetric reduced form voting," Theoretical Economics, Econometric Society.

    More about this item

    Keywords

    Implementation; Reduced-form rules; Auction; Bilateral trade; Mechanism design; Total unimodularity.;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

    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:yor:yorken:19/12. 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: Paul Hodgson (email available below). General contact details of provider: https://edirc.repec.org/data/deyoruk.html .

    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.