Secret vs Public Rings in Common Value Auctions

For a single-object second-price common value auction with colluding bidders, and assuming an ``almost all-inclusive ring", we analyze whether an auctioneer who knows that a bidding ring is present at the auction should reveal their presence, and if so, whether to make the revelation publicly, or secretly to the non-ring bidder. We show that for a family of value functions, and assuming (where possible) that bidders use symmetric strategies, publicly revealing that a ring is present induces the non-ring bidder to submit a bid higher than the amount he bids when he (the non-ring bidder) is convinced that the auction is purely noncooperative. On one hand, this means that conditional on a ring operating at the auction, the auctioneer may improve his position by publicly announcing the ring presence, rather than keeping the ring concealed. On the other hand, this presents a new way that an auctioneer can cheat at the auction without having to employ shills, as even in the absence of colluding bidders, simply inducing bidders to believe that they are facing a ring causes them to bid higher than they would have.