IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v67y2009i1p69-98.html
   My bibliography  Save this article

Worst-case optimal redistribution of VCG payments in multi-unit auctions

Author

Listed:
  • Guo, Mingyu
  • Conitzer, Vincent

Abstract

For allocation problems with one or more items, the well-known Vickrey-Clarke-Groves (VCG) mechanism (aka Clarke mechanism, Generalized Vickrey Auction) is efficient, strategy-proof, individually rational, and does not incur a deficit. However, it is not (strongly) budget balanced: generally, the agents' payments will sum to more than 0. We study mechanisms that redistribute some of the VCG payments back to the agents, while maintaining the desirable properties of the VCG mechanism. Our objective is to come as close to budget balance as possible in the worst case. For auctions with multiple indistinguishable units in which marginal values are nonincreasing, we derive a mechanism that is optimal in this sense. We also derive an optimal mechanism for the case where we drop the non-deficit requirement. Finally, we show that if marginal values are not required to be nonincreasing, then the original VCG mechanism is worst-case optimal.

Suggested Citation

  • Guo, Mingyu & Conitzer, Vincent, 2009. "Worst-case optimal redistribution of VCG payments in multi-unit auctions," Games and Economic Behavior, Elsevier, vol. 67(1), pages 69-98, September.
    • Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:69-98
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(08)00126-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-438, March.
    2. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    3. Yokoo, Makoto & Sakurai, Yuko & Matsubara, Shigeo, 2004. "The effect of false-name bids in combinatorial auctions: new fraud in internet auctions," Games and Economic Behavior, Elsevier, vol. 46(1), pages 174-188, January.
    4. Chakravarty, Surajeet & Kaplan, Todd R., 2013. "Optimal allocation without transfer payments," Games and Economic Behavior, Elsevier, vol. 77(1), pages 1-20.
    5. Graham, Daniel A & Marshall, Robert C, 1987. "Collusive Bidder Behavior at Single-Object Second-Price and English Auctions," Journal of Political Economy, University of Chicago Press, vol. 95(6), pages 1217-1239, December.
    6. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    7. Porter, Ryan & Shoham, Yoav & Tennenholtz, Moshe, 2004. "Fair imposition," Journal of Economic Theory, Elsevier, vol. 118(2), pages 209-228, October.
    8. Bailey, Martin J, 1997. "The Demand Revealing Process: To Distribute the Surplus," Public Choice, Springer, vol. 91(2), pages 107-126, April.
    9. Green, Jerry & Laffont, Jean-Jacques, 1977. "On the revelation of preferences for public goods," Journal of Public Economics, Elsevier, vol. 8(1), pages 79-93, August.
    10. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    11. Goldberg, Andrew V. & Hartline, Jason D. & Karlin, Anna R. & Saks, Michael & Wright, Andrew, 2006. "Competitive auctions," Games and Economic Behavior, Elsevier, vol. 55(2), pages 242-269, May.
    12. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    13. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    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. Simon Loertscher & Leslie M. Marx, 2022. "To sell public or private goods," Review of Economic Design, Springer;Society for Economic Design, vol. 26(3), pages 385-415, September.
    2. Josheski Dushko & Karamazova Elena, 2021. "Auction theory and a note on game mechanisms," Croatian Review of Economic, Business and Social Statistics, Sciendo, vol. 7(1), pages 43-59, May.
    3. Dilip Mookherjee, 2008. "The 2007 Nobel Memorial Prize in Mechanism Design Theory," Scandinavian Journal of Economics, Wiley Blackwell, vol. 110(2), pages 237-260, June.
    4. Sarkar, Soumendu, 2018. "Convergence of VCG mechanism to ex-post budget balance in a model of land acquisition," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 37-46.
    5. Simon Loertscher & Leslie M. Marx, 2022. "Incomplete Information Bargaining with Applications to Mergers, Investment, and Vertical Integration," American Economic Review, American Economic Association, vol. 112(2), pages 616-649, February.
    6. Vijay Krishna & Motty Perry, 1997. "Efficient Mechanism Design," Game Theory and Information 9703010, University Library of Munich, Germany, revised 28 Apr 1998.
    7. Delacrétaz, David & Loertscher, Simon & Marx, Leslie M. & Wilkening, Tom, 2019. "Two-sided allocation problems, decomposability, and the impossibility of efficient trade," Journal of Economic Theory, Elsevier, vol. 179(C), pages 416-454.
    8. Sprumont, Yves, 2013. "Constrained-optimal strategy-proof assignment: Beyond the Groves mechanisms," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1102-1121.
    9. Jeong, Seungwon (Eugene) & Lee, Joosung, 2024. "The groupwise-pivotal referral auction: Core-selecting referral strategy-proof mechanism," Games and Economic Behavior, Elsevier, vol. 143(C), pages 191-203.
    10. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    11. Matsushima, Hitoshi & Noda, Shunya, 2023. "Mechanism design with general ex-ante investments," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    12. Paul Milgrom, 2006. "Package Auctions and Package Exchanges: the 2004 Fisher-Schultz Lecture," Levine's Bibliography 321307000000000131, UCLA Department of Economics.
    13. Martin Bichler & Zhen Hao & Richard Littmann & Stefan Waldherr, 2020. "Strategyproof auction mechanisms for network procurement," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(4), pages 965-994, December.
    14. repec:grz:wpaper:2016-03 is not listed on IDEAS
    15. Marek Pycia & Peter Troyan, 2023. "A Theory of Simplicity in Games and Mechanism Design," Econometrica, Econometric Society, vol. 91(4), pages 1495-1526, July.
    16. Schnizler, Bjorn & Neumann, Dirk & Veit, Daniel & Weinhardt, Christof, 2008. "Trading grid services - a multi-attribute combinatorial approach," European Journal of Operational Research, Elsevier, vol. 187(3), pages 943-961, June.
    17. Kuzmics, Christoph & Steg, Jan-Henrik, 2017. "On public good provision mechanisms with dominant strategies and balanced budget," Journal of Economic Theory, Elsevier, vol. 170(C), pages 56-69.
    18. Joosung Lee, 2017. "Mechanisms with Referrals: VCG Mechanisms and Multilevel Mechanisms," Working Papers 2017.27, Fondazione Eni Enrico Mattei.
    19. Alva, Samson & Manjunath, Vikram, 2020. "The impossibility of strategy-proof, Pareto efficient, and individually rational rules for fractional matching," Games and Economic Behavior, Elsevier, vol. 119(C), pages 15-29.
    20. Shao, Ran & Zhou, Lin, 2016. "Voting and optimal provision of a public good," Journal of Public Economics, Elsevier, vol. 134(C), pages 35-41.
    21. Steven R. Williams, 1994. "A Characterization of Efficient," Discussion Papers 1100, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

    More about this item

    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:67:y:2009:i:1:p:69-98. 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.