Anonymous Bidding and Revenue Maximization

We consider a single indivisible object auctioned in an ascending bid English auction. Two variations of this auction are compared with respect to the seller's revenue. In the first mechanism the participants observe the identity of a bidder that drops from the auction while in the second variation they only observe that someone has dropped, however this bidder remains anonymous. We show that the anonymous mechanism could yield a higher expected revenue to the seller and that, generically, neither auction format dominates the other with respect to revenue maximization.