Corruption in auctions, where an auctioneer engages in bid rigging with one (or several) of the bidders, occurs rather frequently in practice, especially in the public sector (e.g., in construction and procurement auctions). We study the social welfare loss caused by corrupt auctioneers, both in single-item and multi-unit auctions.

In our model, the auctioneer may collude with the winning bidders by letting them lower their bids in exchange for a fraction \gamma \in [0, 1] of the surplus. In the most basic corruption scheme, also known as magic number cheating, all winning bidders lower their bid to the highest losing bid. 

More generally, we consider corruption schemes that can be related to \gamma-approximate first-price auctions, where the payments recover at least a \gamma-fraction of the first-price payments. Our goal is to obtain a precise understanding of the robust price of anarchy (POA) of such auctions.

In this talk, we review some of the techniques to analyze the POA of auctions and discuss their applications and limits to corrupt auction schemes. We derive several (tight) bounds which provide a rather fine-grained landscape of the price of anarchy, depending on the auction setting and the equilibrium notion.

Joint work with Andries van Beek and Ruben Brokkelkamp.