Optimal reserve price in static and dynamic sponsored search auctions

Sponsored search advertising is a significant revenue source for search engines. To ameliorate revenues, search engines often set fixed or variable reserve price to in influence advertisers’ bidding. This paper studies the optimal reserve price for a generalized second-price auction (GSP) under both static and dynamic settings. We show that if advertisers’ per-click value has an increasing generalized failure rate, the search engine’s revenue rate is quasi-concave and hence there exists an optimal reserve price under both settings. Different from a static GSP auction where the optimal reserve price is proved to be constant, in a dynamic setting the optimal reserve price is dependent on not only advertisers’ per-click values, but also the number of ad links sold. A search engine should gradually raise reserve price as more qualified advertisers arrive, and maintain the same threshold after all first-page positions are occupied.