Shill bidding occurs when fake bids are introduced into an auction on the seller’s behalf in to artificially inflate the final price. The seller either has associates bid in the seller’s auctions, or the seller controls multiple fake bidder accounts that are used for shill bidding. We proposed a reputation system referred to as the Shill Score that indicates how likely a bidder is to be engaging in price inflating behaviour in a specific seller’s auctions. A potential bidder can observe the other bidders’ Shill Scores, and if they are high, the bidder can elect not to participate as there is some evidence that shill bidding occurs in the seller’s auctions. However, if a seller is in collusion with other sellers, or controls multiple seller accounts, the seller can spread the risk between the various sellers and can reduce suspicion on the shill bidder. Collusive seller behaviour impacts one of the characteristics of shill bidding the Shill Score examines; consequently, collusive behaviour can reduce a bidder’s Shill Score. This paper extends the Shill Score to detect shill bidding where multiple sellers are working in collusion with each other. We propose the first algorithm to provide evidence of whether groups of sellers are colluding. Based on how tight the association is between the sellers and the level of apparent shill bidding that is occurring in the auctions, a suspect bidder’s Shill Score is adjusted appropriately to remove any advantage from seller collusion. Performance is demonstrated using simulated and commercial auction data and extensive experimental results are presented.

当以卖方的名义将虚假出价引入拍卖以人为抬高最终价格时，就会发生虚假出价。卖家要么在卖家的拍卖中让同事出价，要么卖家控制多个虚假的投标人账户，这些账户用于欺骗投标。我们提出了一种称为Shill Score的声誉系统这表明投标人在特定卖方的拍卖中参与价格上涨行为的可能性有多大。潜在竞拍者可以观察其他竞拍者的Shill score，如果评分高，则竞拍者可以选择不参与，因为有证据表明卖家的拍卖中发生了shill 竞拍。但是，如果卖家与其他卖家勾结，或控制多个卖家账户，卖家可以在各个卖家之间分散风险，减少对骗子投标人的怀疑。串通卖家行为影响了 Shill Score 所考察的恶意竞标的特征之一；因此，串通行为会降低投标人的 Shill Score。本文扩展了 Shill Score 以检测多个卖家相互勾结的欺诈投标。我们提出了第一个算法来提供证据证明卖家群体是否串通。根据卖方之间的联系紧密程度以及拍卖中出现的明显的欺骗性投标水平，适当调整可疑投标者的欺骗性得分，以消除卖方串通的任何优势。使用模拟和商业拍卖数据展示了性能，并提供了广泛的实验结果。