Corruption in auctions is a phenomenon that is theoretically still poorly understood, despite the fact that it occurs rather frequently in practice. In this paper, we initiate the study of the social welfare loss caused by a corrupt auctioneer, both in the single-item and the multi-unit auction setting. In our model, the auctioneer may collude with the winners of the auction by letting them lower their bids in exchange for a fixed fraction $\gamma$ of the surplus. As it turns out, this setting is equivalent to a $\gamma$-hybrid auction in which the payments are a convex combination (parameterized by $\gamma$) of the first-price and the second-price payments. Our goal is thus to obtain a precise understanding of the (robust) price of anarchy of $\gamma$-hybrid auctions. If no further restrictions are imposed on the bids, we prove a bound on the robust POA which is tight (over the entire range of $\gamma$) for the single-item and the multi-unit auction setting. On the other hand, if the bids satisfy the no-overbidding assumption a more fine-grained landscape of the price of anarchy emerges, depending on the auction setting and the equilibrium notion. We derive tight bounds for single-item auctions up to the correlated price of anarchy and for the pure price of anarchy in multi-unit auctions. These results are complemented by nearly tight bounds on the coarse correlated price of anarchy in both settings.
翻译:拍卖中的腐败现象在理论上仍然不为人所理解,尽管实际上经常发生。在本文中,我们开始研究腐败拍卖者在单项和多单位拍卖中造成的社会福利损失。在我们的模型中,拍卖者可能与拍卖胜出者串通,允许他们降低出价以换取固定部分的盈余美元作为交换。事实证明,这一设定相当于美元-合金拍卖,其中付款是第一价和第二价付款的混杂组合(以美元为比值 ) 。因此,我们的目标是准确了解无序价格$\gamma$-稳重拍卖的(rbust)价格。如果不对出价施加进一步限制,我们就会证明对单一项目和多单位拍卖安排的紧凑性POA(超过整价的整价范围 ) 。另一方面,如果标价满足了无序拍卖的定值,那么在一次拍卖的固定价格中,我们就会得出一个固定的正常价格。