A seller is pricing identical copies of a good to a stream of unit-demand buyers. Each buyer has a value on the good as his private information. The seller only knows the empirical value distribution of the buyer population and chooses the revenue-optimal price. We consider a widely studied third-degree price discrimination model where an information intermediary with perfect knowledge of the arriving buyer's value sends a signal to the seller, hence changing the seller's posterior and inducing the seller to set a personalized posted price. Prior work of Bergemann, Brooks, and Morris (American Economic Review, 2015) has shown the existence of a signaling scheme that preserves seller revenue, while always selling the item, hence maximizing consumer surplus. In a departure from prior work, we ask whether the consumer surplus generated is fairly distributed among buyers with different values. To this end, we aim to maximize welfare functions that reward more balanced surplus allocations. Our main result is the surprising existence of a novel signaling scheme that simultaneously $8$-approximates all welfare functions that are non-negative, monotonically increasing, symmetric, and concave, compared with any other signaling scheme. Classical examples of such welfare functions include the utilitarian social welfare, the Nash welfare, and the max-min welfare. Such a guarantee cannot be given by any consumer-surplus-maximizing scheme -- which are the ones typically studied in the literature. In addition, our scheme is socially efficient, and has the fairness property that buyers with higher values enjoy higher expected surplus, which is not always the case for existing schemes.

翻译：一位卖家以单位需求买家的顺序流对同质商品进行定价。每位买家对该商品拥有私人估值，卖家仅知晓买家群体的经验价值分布，并选择收益最优价格。我们考虑一个广泛研究的第三级价格歧视模型：一个对到达买家估值拥有完美知识的信息中介向卖家发送信号，从而改变卖家的后验信念，并诱导其设定个性化标价。Bergemann、Brooks和Morris（《美国经济评论》，2015年）的前期工作已证明存在一种信号方案，既能保持卖家收益不变，又能始终售出商品，从而最大化消费者剩余。与先前研究不同，我们探讨这种消费者剩余是否在不同估值的买家之间公平分配。为此，我们旨在最大化奖励更均衡剩余分配的福利函数。我们的主要结果是发现了一种令人惊讶的新型信号方案：与任意其他信号方案相比，该方案能同时对所有非负、单调递增、对称且凹的福利函数实现$8$倍近似。此类福利函数的经典例子包括功利主义社会福利、纳什福利和最大最小福利。任何消费者剩余最大化方案（即文献中通常研究的方案）都无法提供这种保证。此外，我们的方案具有社会效率，并具备公平性特征：高估值买家获得更高的期望剩余——这在现有方案中并非总能实现。