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Optimal shill bidding in the VCG mechanism

  • Itai Sher

    ()

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://hdl.handle.net/10.1007/s00199-010-0566-6
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Article provided by Springer & Society for the Advancement of Economic Theory (SAET) in its journal Economic Theory.

Volume (Year): 50 (2012)
Issue (Month): 2 (June)
Pages: 341-387

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Handle: RePEc:spr:joecth:v:50:y:2012:i:2:p:341-387
DOI: 10.1007/s00199-010-0566-6
Contact details of provider: Web page: http://www.springer.com

Web page: http://saet.uiowa.edu/

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  1. Paul Milgrom, . "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Working Papers 98002, Stanford University, Department of Economics.
  2. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 393-407, March.
  3. 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.
  4. Soo Chew & Shigehiro Serizawa, 2007. "Characterizing the Vickrey combinatorial auction by induction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 393-406, November.
  5. 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.
  6. 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.
  7. Ruqu Wang & Parimal Kanti Bag & Emim Murat Dinlersoz, 1998. "More on Phantom Bidding," Working Papers 976, Queen's University, Department of Economics.
    • Ruqu Wang & Emin Murat Dinlersoz & Parimal Kanti Bag, 2000. "More on phantom bidding," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 701-707.
  8. Estelle Cantillon & Martin Pesendorfer, 2006. "Auctioning bus routes: the London experience," ULB Institutional Repository 2013/9003, ULB -- Universite Libre de Bruxelles.
  9. 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.
  10. 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.
  11. Marshall, Robert C. & Marx, Leslie M., 2007. "Bidder collusion," Journal of Economic Theory, Elsevier, vol. 133(1), pages 374-402, March.
  12. 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.
  13. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  14. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics.
  15. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847, Junio.
  16. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
  17. 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.
  18. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
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