A robust combinatorial auction mechanism against shill bidders

Abstract

This paper presents a method for discovering and detecting shill bids in combinatorial auctions. The Vickrey-Clarke-Groves Mechanism is one of the most important combinatorial auctions because it can satisfy the strategy-proof property, individual rationality, and Pareto efficiency, that is, it is the only mechanism that simultaneously satisfies these properties. As Yokoo et al. pointed out, false-name bids and shill bids pose an emerging problem for auctions, since on the Internet it is easy to establish different e-mail addresses and accounts for auction sites. Yokoo et al. proved that VCG cannot satisfy the false-name-proof property, and they also proved that no auction protocol can satisfy all three of the above properties and the false-name proof property simultaneously. Their approach concentrates on designing a new mechanism that has desirable properties, but this is quite complicated. As a new approach against shill-bids, in this paper, we design a mechanism that utilizes VCG and an algorithm for finding potential shill bids. Our mechanism is quite simple compared with Yokoo's approaches [11][12][13]. Our mechanism can judge whether there might be a shill bid from the results of the VCG procedure. We prove a theorem stating that shill bidders cannot increase their utilities unless all shill bidders win in the auction. Based on this theorem, our proposed mechanism compares the agents' utilities in a conventional auction with those in an auction where a shill bidder does not join in the auction. When these agents' utilities are different between the above cases, such agents might be shill bidders. Then, our mechanism allocates items to the shill bidders as a group from the set of items obtained through successful bids by the agent in the conventional auction. This process prevents shill bidders from increasing unfair profits. Furthermore, even though shill bidders participate in the auction, the seller's profit does not decrease using our proposed method. Thus, our mechanism detects shill bids when it only detects the possibility of shill bids. Our proposed method has the following three key advantages. First, we propose a method to detect shill bidders by comparison between bidders utilities. Our method is superior than existing complex mechanisms in the point of view of generalization and wide-use, because our auction mechanism employs only VCG. Second, even though there are shill bidders in an auction, incentive compatibility property is preserved using our mechanism. Finally, the schemer, in our mechanism, does never have incentive to make shill bidders. The schemer's utility does not increase in our mechanism even though a schemer make shill bidders. Namely, not to make shill bidders is dominant strategy for the schemer.