Abstract: As an effective resource allocation and price determination mechanism, auction can fully introduce market competition and is widely used in all aspects of social and economic activities. On the basis of the increasingly mature traditional auction, people began to gradually relax the auction hypothesis, thus obtaining results of practical significance. For example, in the classic auction theory summarized by Milgrom, it is assumed that there is no fraud. However, in reality, the general auction participants often lack accurate valuation information, and at the same time, the phenomena of opaque auction procedures and staggered rights relationship are common, which leads to the emergence of auction fraud. In the auction process with low transparency, sellers often choose to implement fraud to increase the selling price due to the temptation of interests, thus obtaining improper profits. The choice of the seller and the strategies of the bidders have become urgent research topics. The changes brought by the seller's fraud to the auction are studied in this paper. As one of the most effective trading mechanisms, it is obvious that there are signal transmission and game process in auction. In this paper, on the basis of previous models of fraud according to probability, a mechanism (realized by Bayesian theorem) for bidders to update their judgment according to the obtained information (seller selection) is added, thus a seller fraud model based on signal game is established. The model assumes two kinds of sellers, one is a fraudulent seller who will enjoy the first bid price in the second price auction using the "hold" bid method. One is an honest seller who will not use fraudulent means. At the beginning of the auction, the seller will choose whether the auction will be conducted at the first price or at the second price (during the auction at the first price, fraudulent sellers cannot commit fraudulent acts). The buyer first refers to the seller's choice and updates his judgment on the seller's type according to Bayesian theorem so as to formulate the quotation strategy. Further study the possible equilibrium solutions of the two strategies. Intuitively, fraudulent sellers will choose the second price auction while honest sellers will choose the first price auction. However, analysis shows that in some cases, fraudulent sellers will choose the first price auction and honest sellers will also choose the second price auction. This paper obtains an equilibrium solution under three circumstances. In some cases, fraudulent sellers will also choose the first price auction, while honest sellers will also choose the second price auction. At the same time, the higher the probability that the seller type is fraudulent, the lower the enthusiasm of the buyer. The higher the buyer's valuation of the goods, the more sensitive his quotation strategy is to the judgment of the seller's type. It has wider practical significance in analyzing and preventing fraudulent auctions.

Key words: seller fraud, first price auction, second price auction, correlation value, bayes theory