Abstract: Based on the latest research on sponsored search auctions by the methodology of static games theory,this article builds a common model of sponsored search auctions by concluding on the value function of advertisers and settling the auctions rules as well.After stating the Nash equilibrium condition,the envy-free equilibrium condition and the relations between the two,it proves that while ranking by income better off than ranking by bids in terms of equilibrium,it does not necessarily bring an increase to the search engines. An arithmetic example is given in the end.

Key words: sponsored search auctions, ranking by income, ranking by bids, GSP auctions