Collusion with Not-So-Secret Rings

When collusion is analyzed for Independent private value auctions, it is implicitly assumed that ring presence is commonly known to colluding and non-colluding bidders. We drop this assumption and analyze a simple model of a first price Independent Private Value auction with uniformly distributed values where a single bidder knows privately of the existence of collusion by others. We show that this knowledge leads him to bid shading (weakly) in the first price auction compared to what he would have bid otherwise. This in turn yields the result that the second price auction dominates the first price auction in terms of seller revenue. This contrasts results from the literature showing that under our framework, when bidding is done while the presence of colluding bidders is common knowledge, the first price auction dominates the second price auction.