We study the power of price discrimination via an intermediary in bilateral trade, when there is a revenue-maximizing seller selling an item to a buyer with a private value drawn from a prior. Between the seller and the buyer, there is an intermediary that can segment the market by releasing information about the true values to the seller. This is termed signaling, and enables the seller to price discriminate. In this setting, Bergemann et al. showed the existence of a signaling scheme that simultaneously raises the optimal consumer surplus, guarantees the item always sells, and ensures the seller's revenue does not increase. Our work extends the positive result of Bergemann et al. to settings where the type space is larger, and where optimal auction is randomized, possibly over a menu that can be exponentially large. In particular, we consider two settings motivated by budgets: The first is when there is a publicly known budget constraint on the price the seller can charge and the second is the FedEx problem where the buyer has a private deadline or service level (equivalently, a private budget that is guaranteed to never bind). For both settings, we present a novel signaling scheme and its analysis via a continuous construction process that recreates the optimal consumer surplus guarantee of Bergemann et al. The settings we consider are special cases of the more general problem where the buyer has a private budget constraint in addition to a private value. We finally show that our positive results do not extend to this more general setting. Here, we show that any efficient signaling scheme necessarily transfers almost all the surplus to the seller instead of the buyer.

翻译：我们研究了双边贸易中通过中介进行价格歧视的能力，此时存在一个追求收入最大化的卖家，向一个拥有先验分布下私有估值的买家出售物品。在卖家与买家之间，存在一个中介，可以通过向卖家释放关于真实价值的信息来分割市场。这被称为信号传递，使卖家能够实施价格歧视。在此背景下，Bergemann 等人证明了存在一种信号方案，能够同时提升最优消费者剩余、确保物品始终售出，并保证卖家收入不会增加。我们的工作将 Bergemann 等人的积极结果扩展到类型空间更大、且最优拍卖是随机化（可能基于指数级大小的菜单）的场景中。具体而言，我们考虑了两种由预算动机驱动的场景：第一种是卖家可收取价格存在公开已知的预算约束；第二种是联邦快递问题，其中买家拥有私有截止日期或服务等级（即私有预算，保证永不失效）。对于这两种场景，我们提出了一种新颖的信号方案，并通过连续构造过程进行分析，复现了 Bergemann 等人对最优消费者剩余的保证。我们研究的场景是更一般问题的特例，其中买家除了私有估值外还拥有私有预算约束。最后，我们证明我们的积极结果无法推广到这一更一般的场景。在此情况下，我们表明任何有效的信号方案都必然将几乎全部剩余转移给卖家而非买家。