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Optimal shill bidding in the VCG mechanism

Itai Sher
Economic Theory
Vol. 50, No. 2 (June 2012), pp. 341-387
Published by: Springer
Stable URL: http://www.jstor.org/stable/41486014
Page Count: 47
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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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