Bidder collusion at first-price auctions

We show that in simple environments, a bidding ring operating at a first-price sealed-bid auction cannot achieve any gains relative to non-cooperative bidding if the ring is unable to control the bids that its members submit at the auction. This contrasts with results for the case in which the ring can control its members’ bids or prevent all but one of the ring members from participating in the auction. Numerical examples suggest that this result extends to some more complex environments. The analytic results use linear programming techniques that have potential applications to a number of other economic problems.