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A simplified mechanism is a direct mechanism modified by restricting the set of reports or bids. An example is the auction used to place ads on Internet search pages, in which each advertiser bids a single price to determine the allocation of eight or more ad positions on a page. If a simplified mechanism satisfies the "best-reply-closure" property, then all Nash equilibria of the simplified mechanism are also equilibria of the original direct mechanism. For search advertising auctions, suitable simplifications eliminate inefficient, low-revenue equilibria that are favored in the original direct mechanism when bidding costs are positive.