A recent development in online advertising has been the ability of advertisers to have their ads displayed exclusively on (a part of) a web page. We study this phenomenon in the context of both sponsored search advertising and display advertising. Ads are sold through auctions, and when exclusivity is allowed, the seller accepts two bids from advertisers, where one bid is for the standard display format in which multiple advertisers are displayed, and the other bid is for being shown exclusively (therefore they are called two-dimensional, or 2D, auctions). We identify two opposing forces at play in an auction that provides the exclusive placement option—allowing more flexible expression of preferences through bidding for exclusivity increases competition among advertisers, leading to higher bids, which increases the seller’s revenue (between-advertiser competition effect), but it also gives advertisers the incentive to shade their bids for their nonpreferred outcomes, which decreases the seller’s revenue (within-advertiser competition effect). Depending on which effect is stronger, the revenue may increase or decrease. We find that the 2D generalized second price (GSP2D) auction, which is an extension of the widely used generalized second price (GSP) auction and on which currently used auctions for exclusive placement are based, may lead to higher or lower revenue under different parametric conditions. Paradoxically, the revenue from allowing exclusive placement decreases as bidders have higher valuations for exclusive placement. We verify several key implications from our analysis of GSP2D using data from Bing for over 100,000 auctions. As a possible solution (applicable to both sponsored search and display advertising), we show that using VCG2D, which is the adaptation of the Vickrey–Clarke–Groves (VCG) auction for the 2D setting, guarantees weakly higher revenue when exclusive display is allowed. This is because it induces truthful bidding, which alleviates the problem of bid shading due to the within-advertiser competition effect.