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Optimal shill bidding in the VCG mechanism

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Abstract

This paper studies shill bidding in the Vickrey–Clarke–Groves (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 (Yokoo et al. Games Econ Behav, 46 pp. 174–188, 2004). 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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Authors and Affiliations

  1. Department of Economics, University of Minnesota, 4-101 Hanson Hall, 1925 Fourth Street South, Minneapolis, MN, 55455, USA

    Itai Sher

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  1. Itai Sher
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Correspondence to Itai Sher.

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I am grateful to Vincent Conitzer, David Rahman, and Tomasz Strzalecki for useful discussions. I am also grateful to seminar participants at The University of Texas at Austin, University of Wisconsin-Madison, University of Oxford, University College London, The London School of Economics and Political Science, The University of Western Ontario, the Midwest Economic Theory Meetings at The Ohio State University, and the Canadian Economic Theory Conference at University of Toronto.

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Sher, I. Optimal shill bidding in the VCG mechanism. Econ Theory 50, 341–387 (2012). https://doi.org/10.1007/s00199-010-0566-6

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