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Optimal Shill Bidding in the VCG Mechanism

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  • Itai Sher

    ()
    (Department of Economics, University of Minnesota)

Abstract

This paper studies shill bidding in the VCG mechanism applied to combinatorial auctions. Shill bidding is a strategy whereby a single decision-maker enters the auction under the guise of multiple identities (Sakurai, Yokoo, and Matsubara 1999). I formulate the problem of optimal shill bidding for a bidder who knows the aggregate bid of her opponents. A key to the analysis is a subproblem--the cost minimization problem (CMP)--which searches for the cheapest way to win a given package using shills. An analysis of the CMP leads to several fundamental results about shill bidding: (i) I provide an exact characterization of the aggregate bids b such that some bidder would have an incentive to shill bid against b in terms of a new property, Submodularity at the Top; (ii) the problem of optimally sponsoring shills is equivalent to the winner determination problem (for single minded bidders)--the problem of finding an efficient allocation in a combinatorial auction; (iii) shill bidding can occur in equilibrium; and (iv) the problem of shill bidding has an inverse, namely the collusive problem that a coalition of bidders may have an incentive to merge (even after competition among coalition members has been suppressed). I show that only when valuations are additive can the incentives to shill and merge simultaneously disappear.

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File URL: http://www.econ.umn.edu/merr/2008_4.pdf
File Function: First version, 2008
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Bibliographic Info

Paper provided by University of Minnesota, Department of Economics in its series Working Papers with number 2008-4.

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Length: 52 pages
Date of creation: 12 2008
Date of revision: 05 2009
Handle: RePEc:min:wpaper:2008-4

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Keywords: VCG mechanism; combinatorial auctions; winner determination problem; collusion.;

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  1. 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.
  2. Paul Milgrom, . "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Working Papers 98002, Stanford University, Department of Economics.
  3. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics.
  4. Ruqu Wang & Parimal Kanti Bag & Emim Murat Dinlersoz, 1998. "More on Phantom Bidding," Working Papers 976, Queen's University, Department of Economics.
  5. Deltas, George, 1999. "When does cheating on mail-in bids pay? A guide for the dishonest auctioneer," Journal of Economic Behavior & Organization, Elsevier, vol. 40(3), pages 313-323, November.
  6. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  7. 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.
  8. S.J. Rassenti & V.L. Smith & R.L. Bulfin, 1982. "A Combinatorial Auction Mechanism for Airport Time Slot Allocation," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 402-417, Autumn.
  9. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
  10. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer, vol. 36(3), pages 393-407, March.
  11. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
  12. Soo Chew & Shigehiro Serizawa, 2007. "Characterizing the Vickrey combinatorial auction by induction," Economic Theory, Springer, vol. 33(2), pages 393-406, November.
  13. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847, October.
  14. Estelle Cantillon & Martin Pesendorfer, 2006. "Auctioning bus routes: the London experience," ULB Institutional Repository 2013/9003, ULB -- Universite Libre de Bruxelles.
  15. 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.
  16. Lehmann, Benny & Lehmann, Daniel & Nisan, Noam, 2006. "Combinatorial auctions with decreasing marginal utilities," Games and Economic Behavior, Elsevier, vol. 55(2), pages 270-296, May.
  17. Graham, Daniel A. & Marshall, Robert C. & Richard, Jean-Francois, 1990. "Phantom bidding against heterogeneous bidders," Economics Letters, Elsevier, vol. 32(1), pages 13-17, January.
  18. Marshall, Robert C. & Marx, Leslie M., 2007. "Bidder collusion," Journal of Economic Theory, Elsevier, vol. 133(1), pages 374-402, March.
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