Abstract:

Auction is a mechanism to allocate market resources and tap the value of commodities. With the development of the Internet and the gradual rise of e-commerce， online auctions have become an important part of auctions. With the rise of online auctions， a hybrid mechanism that combines auctions and sales has emerged on various auction sites， that is， buy-it-now auctions. There are three types of buy-it-now auctions： fixed buy-it-now auctions， temporary buy-it-now auctions and lasting buy-it-now auctions. The lasting buy-it-now auctions discussed in this article include auction and buy-it-now at the same time. Bidders can choose bidding option or execute buy-it-now. After bidders choose the auction， the buy-it-now option will not disappear. Subsequent bidders still have two options： auction and buy it now. The current discussion on buy-it-now auctions is aimed at single-item auctions， and does not take into account the situation of multiple items in a buy-it-now auction. Based on the independent private value model， the multi-unit Vickrey auction mechanism and the lasting buy-it-now auction are combined to establish a multi-item lasting buy-it-now auction model. By analyzing the expected returns of the bidder and the seller， the bidder's equilibrium bidding strategy and the seller's optimal buy-it-now price are obtained， and through numerical analysis， different strategies are given for both auction bidders and sellers to conduct multi-item lasting buy-it-now auctions online and offline on-site lasting buy-it-now auctions according to the number of items.The number of bidders in offline auctions is fixed， while the number of bidders in online auctions is not fixed. For this situation， numerical analysis is carried out on the number of auction items in the online auction situation and the offline auction situation respectively. The following conclusions can be drawn： With the increase of their own valuation， the ability of the bidder to accept the buy-it-now price increases， and the bidder has a higher willingness to accept the buy-it-now price option. As the reserve price set by the seller increases， the bid becomes less attractive to bidders who prefer to choose the buy-it-now option. As the commission rate set by the auction platform increases， the willingness of bidders to bid decreases， making it easier to choose a buy-it-now price. When the seller reasonably sets the buy-it-now price， it can improve its own income compared to when the buy-it-now price is not set. During offline auctions， the bidder chooses the lowest bid price， the best bid price set by the seller， and the seller's highest expected income per item all decrease with the increase in the number of items. In online auctions， the bidder chooses the lowest bid price， the best bid price set by the seller， and the seller's highest expected return per item all increase with the increase in the number of items.Based on the above conclusions， the following suggestions are put forward to the auction platform： The commission rate set by the auction platform for bidders should be reasonable. If the setting is too high， it will reduce the attractiveness of bidders for bidding， reduce the number of bidders’ participation， and make bidders’ bidding strategies more conservative and further reduce platform revenue. The commission rate set by the auction platform for bidders should be reasonable. If the setting is too high， it will reduce the attractiveness of bidders for bidding， reduce the number of bidders’ participation， and make bidders’ bidding strategies more conservative and further reduce platform revenue. The auction platform should make suggestions for online auctions or offline auctions according to the number of auction items of sellers， and increase the amount of commissions collected by the platform by increasing the expected income of the sellers. When the auction platform conducts offline auctions， it should limit the number of auction items of the sellers， and maintain the sellers' single-item income. When the auction platform conducts online auctions， it should make suggestions to the sellers to let them sell the items as much as possible at one time， so that the income of a single item can be as high as possible， so that the platform itself can get more commissions.It is assumed that the bidder only has unit demand， and the subsequent research can be conducted on the bidder's demand for multiple units. If the bidder has demand for multiple units， it needs to submit both price and quantity for auction. This situation is much more complicated.

Key words: multi-item auction, number of auction items, buy-it-now auction, independent private values, expected benefit