Determining Damages from the operation of Bidding Rings: An Analysis of the Post-Auction 'Knockout' Sale

Abstract

Members of a bidding ring often use a private sale among themselves, known as the knockout, to decide who will buy the object that the ring has secured. The difference between the price realized in this private sale and the price paid by the ring in the public auction is divided, on the basis of a linear sharing rule, among the ring members. These side-payments provide an incentive for the ring members to bid higher than they would have in an identical public auction. As a consequence, neither the realized price in the private sale nor the total payments of the winner are unbiased estimates of the price the item would have fetched in the public auction in the absence of collusion. This paper evaluates the extent of this overestimate in the independent private values case, for both first price and second price post-auction knockout sales. Bids are not independent of the sharing rule but transfers from the winning bidder are. Further, bidder payoffs are independent of both the auction format and the sharing rule. Finally, it is shown that the overbidding in the knockout sale is increasing with the dispersion of bidder valuations and is of significant empirical relevance. The results of this paper can be used to obtain an unbiased assessment of the damages inflicted on the seller.