Vickrey Auction

Paying the second-highest bid severs the link between what a bidder says and what they pay, so shading a bid only risks losing an auction that was worth winning. Edelman, Ostrovsky, and Schwarz (2007) and Varian (2007) showed the generalized second-price format used for search ads is not truthful once multiple slots are sold, although it has well-behaved envy-free equilibria. Display advertising moved the other way: Google Ad Manager completed its shift to first-price auctions in 2019, which put bid shading back on the buyer's side. The revenue equivalence theorem says the two formats raise the same expected revenue under symmetric, risk-neutral bidders with independent private values; every real ad market violates at least one of those assumptions, which is where the money moves.