Modeling tacit collusion in auctions

We study tacit collusion, which we interpret as collusion without communication about strategies, in repeated auctions in which bidders can only observe past winners and not their bids. Strategies cannot discriminate among initially nameless bidders until they have become named through winning an auction. We obtain two classes of results: (1) Completely refraining from using names rules out collusion altogether, and even if naming is permitted, as per our definition of tacit collusion, the lack of communication limits collusive strategies and payoffs among impatient bidders. (2) Sufficiently patient bidders can overcome the attainability constraints imposed by lack of communication and obtain approximately the same collusive gain as absent communication.