Consider Myerson's optimal auction with respect to an inaccurate prior, e.g., estimated from data, which is an underestimation of the true value distribution. Can the auctioneer expect getting at least the optimal revenue w.r.t. the inaccurate prior since the true value distribution is bigger? This so-called strong revenue monotonicity is known to be true for single-parameter auctions when the feasible allocations form a matroid. We find that strong revenue monotonicity fails to generalize beyond the matroid setting, and further show that auctions in the matroid setting are the only downward-closed auctions that satisfy strong revenue monotonicity. On the flip side, we recover an approximate version of strong revenue monotonicity that holds for all single-parameter auctions, even without downward-closeness. As applications, we improve the sample complexity upper bounds for various single-parameter auctions.
翻译:将Myerson的最佳拍卖视为之前不准确的拍卖,例如,根据数据估算,这是对真实价值分配的低估。 拍卖商能否预期至少获得真实价值分配更大之前的最佳收入? 当可行的分配形成一个机器人时,这种所谓的强大的收入单一性在单参数拍卖中是已知的。 我们发现,强大的收入单一性无法超越配机环境,并进一步显示,在配机环境下的拍卖是唯一能满足强劲收入单一性的下层封闭拍卖。 在反面方面,我们回收了所有单参数拍卖所持有的强收入单一性近似版本,即使没有下层的距离。作为应用,我们提高了各种单数拍卖的样本复杂性。