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

We introduce a class of mechanisms, called bidding clubs, that allow agents to coordinate their bidding in auctions. Bidding clubs invite a set of agents to join, and each invited agent freely chooses whether to accept the invitation or whether to participate independently in the auction. Agents who join a bidding club first conduct a “pre-auction” within the club; depending on the outcome of the pre-auction some subset of the members of the club bid in the primary auction in a prescribed way. We model this setting as a Bayesian game, including agents’ choices of whether or not to accept a bidding club’s invitation. After describing this general setting, we examine the specific case of bidding clubs for first-price auctions. We show the existence of a Bayes-Nash equilibrium where agents choose to participate in bidding clubs when invited and truthfully declare their valuations to the coordinator. Furthermore, we show that the existence of bidding clubs benefits all agents (including both agent inside and outside of a bidding club) in several different senses.