Analyzing the Privacy of a Vickrey Auction Mechanism

This article studies the properties of a distributed mechanism to perform the Vickrey auction. This mechanism, which was originally presented in López, Núñez, Rodríguez, and Rubio (2004), has the main characteristic that most of the information concerning the bids is kept private for both bidders and the auctioneer without the necessity of any trusted third party. In particular, after the auction is finished, only the value of the second-highest bid and the identity of the highest bidder are publicly revealed. However, in that paper, several questions about the applicability of the protocol were left unanswered. In particular, no implementation was provided. Besides, the analysis of the collusion risk was too brief. In this paper, we address these issues in a deeper way. Let us note that, as it is stated in Brandt and Sandholm (2004), it is impossible to create a completely private mechanism to perform the Vickrey auction. In particular, we identify a gap between the proposed protocol and the complete privacy: If any n-2 bidders and the winning bidder collude, the privacy is lost. Besides, some privacy properties can be broken by chance if some specific situations appear, though the probability of this threat decreases as the number of bidders increases. In addition, we present and analyze a simple implementation of the protocol, and we consider its practical applicability.