AI 中文总结
本文针对k个相同物品的n人拍卖，比较歧视性与统一价格拍卖的拍卖价格信息含量，得出最高阶统计量更优的充分必要条件，为相关拍卖机制的信息传递研究提供了依据。
AI 中文摘要
我们研究了k个相同物品的拍卖，参与竞拍者共n人，每人最多竞拍一个物品。这些物品具有共同但未知的价值，竞拍者会收到关于该价值的私人信号。本文比较了歧视性价格拍卖和统一价格拍卖在传递真实价值方面的信息含量，这里的拍卖价格（而非出价）是传递给外部观察者或投资者的信息。由于两种拍卖都存在对称的单调均衡，该问题可简化为比较样本的最高阶统计量与第k+1阶统计量的信息含量。我们找到了最高阶统计量在莱曼意义上更优的充分条件，这些条件涉及高低信号的信息含量以及物品与竞拍者的比例k/n，且这些条件在定性层面也是必要的。
英文摘要
We study auctions of k identical objects to n bidders, each of whom wants at most one. The objects have a common but unknown value and the bidders receive private signals about this value. The discriminatory price auction and the uniform-price auction are compared in terms of how informative the resulting auction prices (not bids) are in conveying the true value to an outside observer/investor. Since both auctions have symmetric, monotone equilibria, the problem reduces to comparing the informativeness of the highest order statistic of a sample to the (k+1)st highest. We find sufficient conditions under which the highest order statistic is superior---in the sense of Lehmann---in this regard. The sufficient conditions involve the informativeness of high versus low signals and the ratio k/n of objects to bidders. These conditions are also qualitatively necessary.
