We consider a model of third-degree price discrimination, in which the seller has a valuation for the product which is unknown to the market designer, who aims to maximize the buyers' surplus by revealing information regarding the buyer's valuation to the seller. Our main result shows that the regret is bounded by $U^*(0)/e$, where $U^*(0)$ is the optimal buyer surplus in the case where the seller has zero valuation for the product. This bound is attained by randomly drawing a seller valuation and applying the segmentation of Bergemann et al. (2015) with respect to the drawn valuation. We show that the $U^*(0)/e$ bound is tight in the case of binary buyer valuation.

翻译：我们研究了一种三级价格歧视模型，其中卖方对产品具有一个市场设计者未知的估值，市场设计者旨在通过向卖方披露买方估值信息来最大化买方剩余。我们的主要结果表明，后悔值受限于$U^*(0)/e$，其中$U^*(0)$是卖方对产品估值为零时的最优买方剩余。该界限可通过随机抽取卖方估值并应用Bergemann等人（2015）针对该抽取估值所提出的市场分割方法达到。我们证明，在买方估值为二元的情况下，$U^*(0)/e$界限是紧的。