Collison in Unrepeated, First-Price Auctions with an Uncertain Number of Participants

We identify a self-enforcing collusion protocol (a "bidding ring") for non-repeated first-price auctions. Unlike previous work on the topic such as that by McAfee & McMillan [1992] and Marshall & Marx [2007], we allow for the existence of multiple cartels in the auction and do not assume that non-colluding agents have perfect knowledge about the number of colluding agents whose bids are suppressed by the bidding ring. We show that it is an equilibrium for agents to choose to join bidding rings when invited and to truthfully declare their valuations to a ring center, and for non-colluding agents to bid straightforwardly. Furthermore, even though our protocol is efficient, we show that the existence of bidding rings benefits ring centers and all agents, both members and non-members of bidding rings, at the auctioneer's expense.