  Modern commercial Internet search engines display advertisements along side
the search results in response to user queries. Such sponsored search relies on
market mechanisms to elicit prices for these advertisements, making use of an
auction among advertisers who bid in order to have their ads shown for specific
keywords. We present an overview of the current systems for such auctions and
also describe the underlying game-theoretic aspects. The game involves three
parties--advertisers, the search engine, and search users--and we present
example research directions that emphasize the role of each. The algorithms for
bidding and pricing in these games use techniques from three mathematical
areas: mechanism design, optimization, and statistical estimation. Finally, we
present some challenges in sponsored search advertising.
