We examine a formal model of sponsored search in which advertisers can bid not only on search terms, but on search terms under specific contexts. A context is any auxiliary information that might accompany a search, and might include information that is factual, estimated or inferred. Natural examples of contexts include the zip code, gender, or abstract "intentions" (such as researching a vacation) of the searcher. After introducing a natural probabilistic model for context-based auctions, we provide several theoretical results, including the fact that under general circumstances, the overall social welfare of the advertisers and auctioneer together can only increase when moving from standard to context-based mechanisms. In contrast, we provide and discuss specific examples in which only one party (advertisers or auctioneer) benefits at the expense of the other in moving to context-based search.
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