Concavity of order statistics in sample size: Implications for auction design
证明了在单调风险率分布下，期望的第k高顺序统计量关于样本量是凹函数，这保证了在具有凸营销成本的独立私人价值拍卖中，卖方目标函数是凹的，从而存在有限最优解。
I show that the expected k th -highest order statistic from a monotone hazard rate distribution is concave in sample size. In independent private value auctions with convex marketing costs, this ensures that the seller’s objective is concave, yielding a finite optimum. • Highest order statistics are concave in sample size under monotone hazard rate. • Concavity ensures finite optimizers in auction problems with marketing costs. • Results extend to auctions with reserve prices under mild conditions.