论文标题
有限样本平均竞标拍卖
Finite-Sample Average Bid Auction
论文作者
论文摘要
本文研究了拍卖师仅通过统计样本访问评估分布的知识的环境中的拍卖设计问题。建立了一个新的框架，将统计决策理论与机制设计结合在一起。研究了两个最佳标准Maxmin和均衡级，及其对拍卖形式的影响。模棱两可拍卖的最简单形式是平均竞标拍卖，该拍卖的设定与其他投标和历史样本的平均值成正比。这种拍卖形式可以是由伽马分布的动机，它为最佳价格（不规则参数的估计）提供了新的启示。理论结果表明，通常可以使用常规参数总体均值来近似最佳价格。在此想法下开发了自适应平均投标估计器，并且其具有与经验的米尔森估计量相同的渐近特性。新提出的估计器在风险的价值方面的性能明显更好，当样本量较小时预期的不足。
The paper studies the problem of auction design in a setting where the auctioneer accesses the knowledge of the valuation distribution only through statistical samples. A new framework is established that combines the statistical decision theory with mechanism design. Two optimality criteria, maxmin, and equivariance, are studied along with their implications on the form of auctions. The simplest form of the equivariant auction is the average bid auction, which set individual reservation prices proportional to the average of other bids and historical samples. This form of auction can be motivated by the Gamma distribution, and it sheds new light on the estimation of the optimal price, an irregular parameter. Theoretical results show that it is often possible to use the regular parameter population mean to approximate the optimal price. An adaptive average bid estimator is developed under this idea, and it has the same asymptotic properties as the empirical Myerson estimator. The new proposed estimator has a significantly better performance in terms of value at risk and expected shortfall when the sample size is small.
