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中文摘要：
针对英式拍卖、首价密封价格投标拍卖和次价密封价格拍卖的特点，以及欺诈的网络环境中3种拍卖方式下最可能出现的欺诈类型，分析了诚实投标者赢得拍卖的概率和其贝叶斯纳什均衡投标策略。数值计算了这3种投标方式下的投标者期望收益和拍卖方期望收益损失。通过计算结果的比较得到欺诈环境下，分别采用这3种拍卖方式时，投标者期望收益和拍卖方期望收益损失和投标者人数、欺诈概率、投标者估价函数等关系的一般结论。同时也表明，在欺诈的网络环境下，采用英式拍卖，投标者将获得最大的期望收益，而拍卖方也将获得最小的期望收益损失，所以，英式拍卖在网络欺诈环境下仍然是一种流行的拍卖方式。
英文摘要：
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. Af- ter 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 rev- enue and ＇the sellers get the minimal expected revenue loss under English auction. So English auction is the popular auction under the online fraud.
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