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This paper studies the incentives of the seller and buyers to shill bid in a single-item auction. An auction is seller identity-compatible if the seller cannot profit from pretending to be one or more bidders via fake identities. It is buyer identity-compatible if no buyer profits from posing as more than one bidder. Lit auctions reveal the number of bidders, whereas dark auctions conceal the information. We characterize three classic selling mechanisms—first-price, second-price, and posted-price—based on identity compatibility. We show the importance of concealing the number of bidders, which enables the implementation of a broader range of outcome rules. In particular, no optimal lit auction is ex-post seller identity-compatible, while the dark first-price auction (with reserve) achieves the goal.
