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 reserve 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 non-parametric approach to estimate the underlying consumer valuation distribution based on this data. Previous 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：本文聚焦于在线第二价格拍卖，其中竞拍者依次出价，获胜者需支付第二高价与卖方设定的保留价中的较高值。在此类拍卖中，卖方通常无法观察到所有出价或参与竞拍的总人数，仅能获取拍卖过程中的当前成交价格。我们提出了一种新颖的非参数估计方法，基于此类数据推断潜在的消费者估值分布。现有文献中的非参数方法仅利用最终成交价格，并假设已知竞拍者总数。特别地，卖方可利用我们得到的估计结果计算该产品的最优利润最大化价格。该方法无需调整参数，我们通过多种模拟场景及eBay平台Xbox 7日拍卖数据集验证了其计算与统计效率。