Modeling Tacit Collusion in Auctions

We study tacit collusion in repeated auctions in which bidders can only observe past winners and not their bids. We adopt a stringent interpretation of tacit collusion as collusion without communication about strategies that we model as a symmetry restriction on repeated game strategies: Strategies cannot discriminate among initially nameless bidders until they have become named through winning an auction. We obtain three classes of results: (1) Completely refraining from using names, i.e. strengthening the symmetry constraint, 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) If communication is allowed, there are sustained improvements over bid rotation and competitive bidding among patient bidders. (3) These gains extend to tacit collusion among patient bidders. However, whether tacit or not, collusion need not be efficient. ∗ This paper has been previously circulated under the title Tacit Collusion in Repeated Auctions. We thank William Gillespie, Hans Haller, Nancy Lutz, Tomas Sjöström, Xavier Vives, Christian Wey and seminar audiences at Bilkent University, Canadian Economic Theory Meetings (Toronto 2002), ESSET (Gerzensee 2002), Freie Universität Berlin, Humboldt Universität zu Berlin, Pennsylvania State University, Rice University, Universitat Autònoma de Barcelona, Universität zu Mannheim, University College London, Virginia Polytechnic Institute and State University, and the Midwest Economic Theory Meetings (State College 2001) for comments.