We focus on online second price auctions, where bids are made sequentially, and the winning bidder pays the maximum of the second-highest bid and a seller specified starting price. For many such auctions, the seller does not see all the bids or the total number of bidders accessing the auction, and only observes the current selling prices throughout the course of the auction. We develop a novel semi-parametric approach to estimate the underlying consumer valuation distribution based on this data. Previous semi-parametric or non-parametric approaches in the literature only use the final selling price and assume knowledge of the total number of bidders. The resulting estimate, in particular, can be used by the seller to compute the optimal profit-maximizing price for the product. Our approach is free of tuning parameters, and we demonstrate its computational and statistical efficiency in a variety of simulation settings, and also on an Xbox 7-day auction dataset on eBay.

翻译：本文研究在线第二价格拍卖，其中竞价按顺序进行，获胜者支付第二高出价与卖方设定的起拍价之间的较高值。在此类拍卖中，卖方通常无法观测全部出价或参与拍卖的总竞标人数，仅能观察到拍卖过程中的实时成交价。基于此数据，我们提出了一种新颖的半参数方法来估计潜在的消费者价值分布。文献中已有的半参数或非参数方法仅利用最终成交价，且需已知竞标总人数。本方法所得估计结果可供卖方用于计算产品利润最大化的最优定价。该方法无需调节参数，我们在多种模拟场景及eBay上的Xbox七日拍卖数据集上验证了其计算效率与统计效能。