基于二层规划的序贯拍卖中的数量折扣研究

在研究两阶段序贯二价拍卖时，为提高卖者的收益而将数量折扣引入到序贯拍卖中，该问题本质上是一个二层规划问题. 首先推导出买者的均衡报价战略，然后建立了卖者的规划问题并对其进行求解得到最优的数量折扣，最后研究了最优数量折扣下的价格趋势问题. 分析结果表明能否通过采取数量折扣来增加卖者的期望收益取决于两个因素：引入数量折扣能否增加买者的报价以及物品有无可能被分配给不同买者，这对组织拍卖活动有着重要的指导意义.

Research on quantity discount in sequential auctions based on bi-level programming

In order to improve the seller's ex ante expected revenue in a two-stage sequential auction, this paper introduces quantity discount into sequential auction and the problem is a bi-level programming problem essentially. We derive the buyers' equilibrium bidding strategies, then set up the seller's programming problem and obtain the optimal quantity discount by solving it. In the end, the price trend under the optimal quantity discount is studied. Analysis results show that whether adopting quantity discount can improve the seller's expected revenue depends on two factors: whether quantity discount can induce higher bids for the buyers and whether two objects can be allocated to different buyers, which has an important instructive significance in organizing auctions.