具有贝叶斯卖家的价格歧视限制
The Limits of Price Discrimination with a Bayesian Seller
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中文总结 AI 辅助
研究生产成本为贝叶斯且卖家私有时三级价格歧视的限制，推广前人工作。表明可实现的福利结果区域与多面体投影重合，给出计算最优市场细分的多项式时间算法，还建立了市场可写成极值市场凸组合的结构性质。
中文摘要 AI 辅助
我们研究了生产成本为贝叶斯且卖家私有的情况下三级价格歧视的限制，推广了Bergemann、Brooks和Morris（2015）的开创性工作。大致设置如下：垄断卖家为市场不同“细分”中的买家设定不同价格以最大化卖家剩余。市场分解为细分的不同方式会导致不同的福利结果，即（卖家剩余，买家剩余）对。当生产成本是贝叶斯时，可实现的福利结果区域可能呈现出比固定成本情况下Bergemann等人更复杂的形状。我们表明，对于贝叶斯成本，该区域与由多项式数量的线性约束定义的多面体的适当投影重合，其中基本约束对应于“折扣”流网络中的流量守恒。因此，我们给出了一种多项式时间算法，可根据卖家剩余和买家剩余的任何线性组合计算最优市场细分。在此过程中，我们建立了以下结构性质：任何市场都可以写成“极值市场”的凸组合，同时保留卖家剩余和买家剩余。这些极值市场在不同可能成本下是分段等剩余的，推广了Bergemann等人在成本固定时引入的类似概念。
英文摘要
We study the limits of third-degree price discrimination when the production cost is Bayesian and private to the seller, generalizing the seminal work of Bergemann, Brooks and Morris (2015). The rough setup is the following: A monopoly seller sets different prices for buyers in different "segments" of the market so as to maximize seller surplus. Different ways in which the aggregate market is decomposed into segments lead to different welfare outcomes, i.e., (seller surplus, buyer surplus) pairs. When the production cost is Bayesian, the region of achievable welfare outcomes can exhibit complex shapes beyond the clean characterization by Bergemann, Brooks and Morris for the case with a fixed cost. We show that with a Bayesian cost, this region coincides with a proper projection of a polytope defined by a polynomial number of linear constraints, the essential ones of which correspond to flow conservation in a "discounted" flow network. As a result, we give a polynomial-time algorithm that computes optimal market segmentations in terms of any linear combination of the seller surplus and the buyer surplus. En route, we establish the following structural property: Any market can be written as a convex combination of "extremal markets" in a way preserving the seller surplus and the buyer surplus. These extremal markets are piecewise equal-surplus with respect to different possible costs, generalizing a similar notion introduced by Bergemann, Brooks and Morris when the cost is fixed.
