Credible Auctions: A Trilemma

Consider an extensive‐form mechanism, run by an auctioneer who communicates sequentially and privately with bidders. Suppose the auctioneer can deviate from the rules provided that no single bidder detects the deviation. A mechanism is credible if it is incentive‐compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first‐price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy‐proof mechanism.