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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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Suggested Citation

  • Itai Sher, 2012. "Optimal shill bidding in the VCG mechanism," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 341-387, June.
  • Handle: RePEc:spr:joecth:v:50:y:2012:i:2:p:341-387 DOI: 10.1007/s00199-010-0566-6

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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Dominic Herzog, 2014. "Shill Bidder's Behavior in a Second-Price Online Auction," Working papers 2014/03, Faculty of Business and Economics - University of Basel.

    More about this item


    Shill bidding; VCG mechanism; Combinatorial auctions; Winner determination problem; Collusion; C72; D44;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions


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