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

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  • Guo, Mingyu
  • Conitzer, Vincent
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 67 (2009)
    Issue (Month): 1 (September)
    Pages: 69-98

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    Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:69-98

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    Web page: http://www.elsevier.com/locate/inca/622836

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    1. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    2. Bailey, Martin J, 1997. " The Demand Revealing Process: To Distribute the Surplus," Public Choice, Springer, vol. 91(2), pages 107-26, April.
    3. 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 1217-39, December.
    4. 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 427-38, March.
    5. Chakravarty, Surajeet & Kaplan, Todd R., 2006. "Optimal Allocation without Transfer Payments," MPRA Paper 18481, University Library of Munich, Germany, revised 02 Mar 2009.
    6. 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.
    7. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    8. 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.
    9. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
    10. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
    11. Porter, Ryan & Shoham, Yoav & Tennenholtz, Moshe, 2004. "Fair imposition," Journal of Economic Theory, Elsevier, vol. 118(2), pages 209-228, October.
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    Cited by:
    1. Geoffroy de Clippel, 2010. "Copmment on Egalitarianism under Incomplete Information," Working Papers 2010-4, Brown University, Department of Economics.
    2. Geoffroy de Clippel & David Pérez-Castrillo & David Wettstein, 2010. "Egalitarian Equivalence under Asymmetric Information," UFAE and IAE Working Papers 813.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    3. Geoffroy de Clippel & Louis Putterman & Victor Naroditskiy & Maria Polukarov & Amy Greenwald & Nicholas R. Jennings, 2012. "Destroy to Save," Working Papers 2012-9, Brown University, Department of Economics.
    4. Gershkov, Alex & Moldovanu, Benny, 2010. "Efficient sequential assignment with incomplete information," Games and Economic Behavior, Elsevier, vol. 68(1), pages 144-154, January.
    5. Manipushpak Mitra & Arunava Sen, 2010. "Efficient allocation of heterogenous commodities with balanced transfers," Social Choice and Welfare, Springer, vol. 35(1), pages 29-48, June.

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