| Auction theory is one of the success of economics,no matter from the practical experience and theory research,the auction is very important.But the existing auction theory mostly focused on the analysis of a single inseparable item auction or the analysis of auctions in which bidders are single demand.This theory can not be fit for present auction.With the development of society and electronic commerce,the market of auction is various.Lots of inseparable items are sold via auction,the suitable theory need to be explored.As one of mechanism that multiple and inseparable items are sold,the sequential auctions have very important research value.Based on the historical documents and research results,several problem of sequential auction are probed through equilibrium analysis and mechanism design.Firstly,based on nonlinear demand function of bidders,we study the multi-stage sequential auction mechanism of continuous homogeneous divisible goods under uniform price.In this mechanism,the auction process is divided into multiple stages,all bidders are allowed to submit more than once bidding in each stage.If a bidder does not obtain the quantity he wants in former stage auction,he still have another opportunity to obtain some quantity in the later stage auction.For this mechanism,we explore the formation process and composition of equilibrium points in each stage auction,and discuss the optimal strategy selection for bidders.The mechanism can effectively reduce many underpricing equilibrium.It also can avoid the occurrence of failure auction(equilibrium does not exist),and effectively extend and improve the traditional single stage uniform price auction mechanism.Secondly,a sequential auction with information transmission and learning is studied.In the course of the auction,information about the bidders’ values becomes available as winning bids are revealed.From this,bidders can learn about their opponents’ types.So the effects of information transmission and learning are generated.One effect of information is bidders can learn their opponents’ value directly,another more subtle effect of information is that bidders anticipate the generation of information and take this into account in the first auction.The equilibrium in this model is contrasted to a scenario in which bidders are unaware of informational effects.It is shown that the equilibrium strategies first-degree stochastically dominate the ones for the benchmark auction.The dependence of the equilibrium strategies on parameters are showed and the existence of separating equilibrium is provided(In the first auction the bidders with high type do not imitate the bidder with lower type).At last,a dynamic market in which buyers compete in a sequence of auctions for goods.New buyers and new objects may arrive at random times.Since objects are imperfect substitutes,buyers’ values are not persistent.Instead,each buyer’s privatevalue for a new object is a new independent draw from the same distribution.Three problems are studied in this environment.The first direction considering reserve price,a dynamic market in which bidders compete in a sequence of auctions is described.Bidders and objects may arrive to the market randomly.These objects are sold by the first-price auctions with reserve price.Then we demonstrate that if there is no reserve price,the expected value for bidders in first-price sequential auctions is the same as the one in second-price sequential auctions.According to the explicit expression of Markov equilibrium in first-price auction,we illustrate that the expected value with reserve price is less than the one without reserve price.But when the number of bidders is infinite,the reserve price is trivial.That is,if the number of bidders is very more,the competition is very fierce and it is can be avoided that the winning bid is less than the reverse price.The second direction,a dynamic market in which multiple sellers and buyers arrive at random times is described.The equilibrium payoff and the ant-expected value are studied.In real life,multiple sellers will sell their goods at the same time,and multiple buyers will purchase the goods simultaneously.Since the market of multiple sellers is very difficult,we consider the dynamic market in which two sellers and multiple buyers arrive at random times.The third direction,we characterize the dynamic market in which supply is far less than demand.We consider the use of the second-price auctions for selling these objects,then we have the corresponding high-order difference equation when there are multiple new arriving bidders in one period.By changing the high order difference equation into a first-order system of difference equation,we obtain the general solution of the ant expected value.At last by the matrix norm the boundary condition is provided,and in this boundary condition the solution is bounded. |
