English auction, first-price sealed-bid, and second-price sealed-bid auction are three common online auctions. Their characters and the probable cheating styles under each auction were discussed. The honest bidder's winning probability and their Nash equilibrium strategy under each auction were analyzed and their expected gain and the honest seller's revenue loss were calculated. After the results compared,  some general conclusions are given, including the relationships among the bidder's expected gain, the seller's revenue loss, the number of the bidders, the cheating probability and the evaluation functions,  It is also indicated that the bidders can gain the maximal expected revenue and the sellers get the minimal expected revenue loss under English auction. So  English auction is the popular auction under the online fraud.