Optimal reserve price in dynamic sponsored search auction

We study how the search engine should update its reserve price in a sponsored search auction for a particular keyword given a certain number of ad links are sold. Different from a static 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.