基于非齐次泊松过程的网上持久型一口价拍卖研究

Research on lasting buy-it-now auction in online auctions based on inhomogeneous poisson process

为了刻画网上拍卖中的投标者到达过程中存在的末尾抢标机制,本文引入时间变量,建立了基于投标者到达的非齐次泊松过程的持久型一口价拍卖模型。通过令投标人与拍卖商的收益最大化,本文分析了投标人的均衡策略,拍卖商的最优一口价以及拍卖平台的最优佣金率,得到拍卖平台为了获取更多的佣金,一口价拍卖中佣金率的设定应小于普通拍卖中的佣金率。通过数值分析得到,投标人应在持续时间较短的一口价拍卖中积极选择一口价,在持续时间较长的一口价拍卖中更倾向于选择进行竞价,而拍卖商应尽可能地设置更长的拍卖持续时间以此获得更大的期望收益。

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.Different from traditional auctions,the arrival process of bidders in online auctions is random in time and the amount of bids will increase rapidly when online auctions are about to end.Online auctions usually set an end time.In order to attract more bidders,the auction duration of online auctions is longer than that of traditional 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.At present,the discussion about the buy-it-now auction is to fix the number of bidders or make the number of bidders follow the Poisson distribution,without considering the bidding mechanism at the end of the online auction.This article will introduce the auction time and simulate the arrival process of bidders by a non-homogeneous Poisson process.Then it discusses the strategies of bidders,sellers and auction platforms,explores how the auction time affects the strategies of bidders and sellers,and gives suggestions to both bidders and sellers.Based on the assumption of the independent private value model,this article first studies the balanced bidding strategy when bidders choose bidding options.The inhomogeneous Poisson process is used to introduce the auction duration,and compare the expected benefits of choosing the bidding option and executing the buy-it-now option.When the expected returns of the two are equal,there is no difference between the bidding option and the buy-it-now option for the bidder,so the bidder′s buy-it-now price level can be obtained.When the seller sets a buy-it-now price higher than the bidder′s buy-it-price level,the bidder will choose to bid,otherwise the bidder will choose to implement the buy-it-now option.And then by calculating the first-order derivative of the buy-it-now price level,it can be found that the bidder′s buy-it-now price level increases with the increase in its valuation,with the reserve price set by the seller,and with the commission rate set by the auction platform.Bidders with higher valuations are more likely to choose the buy-it-now option,and the higher the reserve price,the bidding will be less attractive to bidders,and it is easier for bidders to choose the buy-it-now option.The increase in the commission rate will also reduce the interest of bidders in bidding option,making them more willing to choose to implement the buy-it-now option.In addition,the game between bidders and sellers can be regarded as a dynamic game.The seller sets a buy-it-now price first,and then the bidder decides on his or her own equilibrium strategy.It can be seen from the reverse recursion method that the seller determines his or her expected return after knowing the bidder′s strategy.By maximizing the seller′s expected profit,he or she can get the best buy-it-now price he or she should set.By comparing the seller′s expected return between not setting a buy-it-now price and setting the optimal buy-it-now price,it is found that the seller can increase his or her expected return by setting a reasonable buy-it-now price.By maximizing the expected revenue of the auction platform,the optimal commission rate that the auction platform should set is obtained.Considering that the auction platform cannot know the buy-it-now price and reserve price set by the seller in advance,and by comparing the best commission rate of the auction platform when the seller sets the buy-it-now price and does not set the buy-it-now price,it is found that the auction platform can set the commission rate lower than the commission rate when there is no buy-it-now option to get more income.At last,through the numerical analysis of the auction duration,it is found that the bidder accepts the lowest private value of the buy-it-now option,the best buy-it-now price that the seller should set,and the seller′s expected benefit increase with the increase of the auction duration.Therefore,some suggestions can be made to sellers and bidders:in the online lasting buy-it-now auction,sellers should set a reasonable buy-it-price.Setting the buy-it-price too high will reduce their own income.Sellers should try to increase the duration of the auction as much as possible to increase the expected return.And as the duration increases,the buy-it-now price should be increased accordingly.Bidders should be more decisive in choosing the buy-it-now option in the lasting buy-it-now auctions with a shorter duration,and choose to bid in the long-lasting buy-it-now auction.