| Along with the inception of the Internet, Online auctions have become popular. There will be a lot of contrasts compared online auction with a short history with its rapid development, which made great concern to experts and scholars of. A rich source of research topics are suggested for economists who would like to know the use of various trading mechanisms in practice. Online auction provides the ideal experimental site for various economic theories as well. It makes the research about online auction theory inevitable. Based on online auction, we take the traditional auction theory, game theory, and probability theory and other mathematical knowledge as a research tool to study of a new online auction, buyout price English auction. And we also make in-depth analysis about the last-minute bidding. Main contents can be summarized in the following aspects:1 Compared with traditional auctions, online auctions make mode of innovation continuously. Online auctions with buyout price, as a mode of the online auction innovation, are widely used because of breaking the auction end of fixed time limits. There are several online auctions with buyout price, and three of them are typical. They are fixed buyout price, temporary buyout price and permanent buyout price respectively. Bidders' strategies decide the ultimate outcome of the auction, which are one of the research emphases of auction theory. Under the independent private valuation model the optimal choice of the bidder with higher valuation than buyout price is to use the buyout price option early in fixed buyout price auction; there is an equilibrium which makes the bidder with higher valuation than the equilibrium use the buyout price option in temporary buyout price auction; threshold function and an equilibrium are existed in permanent buyout price auction, in which the optimal choice of the bidder with higher valuation than the equilibrium or valuation meeting the threshold function is to use the option of buyout price.2 Under the affiliated valuation model, there is no choice of the optimal strategy because of the interplay among the bidders. Bidders with higher valuation than buyout price do not immediately choose a buyout price option, but they wait-and-see to get the other bidders' information, so late bidding is the wiser choice in fixed buyout price auction; there is a still equilibrium in temporary buyout price auction, and the determination of equilibrium is affected by the other bidders' information, and the bidder with higher valuation than the equilibrium does not use the option of the buyout price; in permanent buyout price auction there are threshold function and equilibrium that are affected by the other bidders' information, so the bidder who has the valuation meeting the threshold function or higher valuation than the equilibrium can't choose the buyout price option. Compared with the bidders' strategies in three auctions with buyout price which are under different models: the independent private valuation model and the affiliated valuation model, we find a great deal of change, and then analyze it.3 From the viewpoint of seller, the choice of what kind of a buyout price auction to make itself the greatest benefits is an important consideration. So after the seller deciding to adopt a buyout price auction, he face a question about setting a suitable parameter of the auction-- buyout price, that is the optimization of the buyout price, to obtain the max utility. In our dissertation we discuss the optimization problem of buyout price in the three different auctions with buyout price. And then we analyze the seller's profit under the optimal buyout price respectively. How will the profit in the three different auctions with buyout price under the independent private model? After the numerical analysis we conclude: the profit of temporary buyout price is the biggest, permanent buyout price second, and the final is the fixed buyout price. Finally, we use fixed buyout price English auction as an example and get some conclusions. With the buyout price increasing, the seller's revenue is increasing. Until the optimal buyout price, the seller's revenue is declining. With the buyout price increasing, the probability of non-transaction goods is increasing. With the number of customers increasing, the seller's revenue is increasing.4 The popular of last-minute bidding in online auctions arouse great concern to the people. Some scholars do researches through different point, and then they achieve certain results. In the dissertation we study the bidders' strategies in different end rules under the independent private model and affiliated valuation model respectively. The conclusions are: the sniping is more easily appeared in the auction with "hard" end rule, but does not in the auction with "soft" end rule under the independent private model. The bidders with more informed knowledge and experience choose to bid at the last moment in "hard" end rule, but they will not win in "soft" end rule under affiliated valuation model. Then we study the auction revenue in different auction end rules. The buyers can obtain more additional revenue through the method of bidding at the last moment in the auction with "hard" rule, then the seller's expected profit is damaged. In the auction with "soft" rule the buyers can only bid according to their valuation and can not obtain the additional revenue. So the seller's profit can be maximized because of the object being given the bidder who has the biggest valuation.
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