Abstract: This paper discusses the bidding rank of search engines based on GSP auction in an incomplete information setting,differently from extensively studied by the literature in a complete information setting.Based on static game theory,the existence and performance of Bayes-Nash equilibrium of advertisers on GSP auction and its sufficient condition about click through rate have been discussed.The relation among click through rate and existence of equilibrium has been analyzed.Lastly the effects of click-through on the search engine's revenue have been analyzed.Interestingly,our results are in sharp contrast with the previous literature that adopts a complete information framework and provide decision basis for bidding strategy of bidders and auction mechanism of search engine under incomplete information.

Key words: GSP auction, bidding rank, bayes-nash equilibrium, incomplete information