IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v113y2019icp4-16.html
   My bibliography  Save this article

A universally-truthful approximation scheme for multi-unit auctions

Author

Listed:
  • Vöcking, Berthold

Abstract

We present a randomized incentive-compatible polynomial-time approximation scheme for multi-unit auctions. For every fixed ϵ>0, the approximation scheme provides a polynomial-time algorithm approximating the optimal social welfare within a factor of 1−ϵ. Our mechanism is truthful in the universal sense, i.e., it is a distribution over deterministically truthful mechanisms. It employs VCG payments in a non-standard way as the underlying deterministic mechanisms are not maximal in range and do not belong to the class of affine maximizers. Instead, each of them is composed of a collection of affine maximizers, one for each bidder. This yields a subjective variant of VCG in which payments for different bidders are defined on the basis of possibly different affine maximizers.

Suggested Citation

  • Vöcking, Berthold, 2019. "A universally-truthful approximation scheme for multi-unit auctions," Games and Economic Behavior, Elsevier, vol. 113(C), pages 4-16.
    • Handle: RePEc:eee:gamebe:v:113:y:2019:i:c:p:4-16
    DOI: 10.1016/j.geb.2013.12.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825613001735
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2013.12.007?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. Carbajal, Juan Carlos & McLennan, Andrew & Tourky, Rabee, 2013. "Truthful implementation and preference aggregation in restricted domains," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1074-1101.
    2. Mu'alem, Ahuva & Nisan, Noam, 2008. "Truthful approximation mechanisms for restricted combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 64(2), pages 612-631, November.
    3. G. L. Nemhauser & Z. Ullmann, 1969. "Discrete Dynamic Programming and Capital Allocation," Management Science, INFORMS, vol. 15(9), pages 494-505, May.
    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. Fujimoto, Masako & Yamada, Takeo, 2006. "An exact algorithm for the knapsack sharing problem with common items," European Journal of Operational Research, Elsevier, vol. 171(2), pages 693-707, June.
    2. Christian Meier & Dennis Kundisch & Jochen Willeke, 2017. "Is it Worth the Effort?," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 59(2), pages 81-95, April.
    3. Shahar Dobzinski & Noam Nisan & Michael Schapira, 2005. "Truthful Randomized Mechanisms for Combinatorial Auctions," Discussion Paper Series dp408, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. Jamain, Florian, 2014. "Représentations discrètes de l'ensemble des points non dominés pour des problèmes d'optimisation multi-objectifs," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14002 edited by Bazgan, Cristina.
    5. Alexandre D. Jesus & Luís Paquete & Arnaud Liefooghe, 2021. "A model of anytime algorithm performance for bi-objective optimization," Journal of Global Optimization, Springer, vol. 79(2), pages 329-350, February.
    6. Bian, Zheyong & Liu, Xiang, 2019. "Mechanism design for first-mile ridesharing based on personalized requirements part II: Solution algorithm for large-scale problems," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 172-192.
    7. M. Yenmez, 2015. "Incentive compatible market design with applications," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 543-569, August.
    8. Wilbaut, Christophe & Todosijevic, Raca & Hanafi, Saïd & Fréville, Arnaud, 2023. "Heuristic and exact reduction procedures to solve the discounted 0–1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 304(3), pages 901-911.
    9. Bagloee, Saeed Asadi & Asadi, Mohsen, 2015. "Prioritizing road extension projects with interdependent benefits under time constraint," Transportation Research Part A: Policy and Practice, Elsevier, vol. 75(C), pages 196-216.
    10. De, Parikshit & Mitra, Manipushpak, 2019. "Balanced implementability of sequencing rules," Games and Economic Behavior, Elsevier, vol. 118(C), pages 342-353.
    11. Jon X. Eguia & Dimitrios Xefteris, 2021. "Implementation by Vote-Buying Mechanisms," American Economic Review, American Economic Association, vol. 111(9), pages 2811-2828, September.
    12. Jarman, Felix & Meisner, Vincent, 2017. "Ex-post optimal knapsack procurement," Journal of Economic Theory, Elsevier, vol. 171(C), pages 35-63.
    13. Babaioff, Moshe & Blumrosen, Liad, 2008. "Computationally-feasible truthful auctions for convex bundles," Games and Economic Behavior, Elsevier, vol. 63(2), pages 588-620, July.
    14. Paul Dütting & Vasilis Gkatzelis & Tim Roughgarden, 2017. "The Performance of Deferred-Acceptance Auctions," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 897-914, November.
    15. Fasil Alemante & Donald E. Campbell & Jerry S. Kelly, 2016. "Characterizing the resolute part of monotonic social choice correspondences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 765-783, October.
    16. Dobzinski, Shahar & Nisan, Noam, 2015. "Multi-unit auctions: Beyond Roberts," Journal of Economic Theory, Elsevier, vol. 156(C), pages 14-44.
    17. Dütting, Paul & Talgam-Cohen, Inbal & Roughgarden, Tim, 2017. "Modularity and greed in double auctions," Games and Economic Behavior, Elsevier, vol. 105(C), pages 59-83.
    18. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    19. Ye Tian & Miao Sun & Zuoliang Ye & Wei Yang, 2016. "Expanded models of the project portfolio selection problem with loss in divisibility," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(8), pages 1097-1107, August.
    20. Bin Li & Dong Hao & Dengji Zhao, 2020. "Incentive-Compatible Diffusion Auctions," Papers 2001.06975, arXiv.org, revised Apr 2020.

    More about this item

    Keywords

    Mechanism design; Multi-unit auctions; Universal truthfulness;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

    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:eee:gamebe:v:113:y:2019:i:c:p:4-16. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.