Nonlinear pricing with finite information

• 成果类型: Article
• 署名作者: Bergemann, Dirk; Yeh, Edmund; Zhang, Jinkun
• 署名单位: Yale University; Northeastern University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2021.08.004
• 发表日期: 2021
• 页码: 62-84
• 关键词: Mechanism design; nonlinear pricing; Multi-dimension; Multi-product; private information; Limited information; QUANTIZATION; Information theory

摘要

We analyze nonlinear pricing with finite information. We consider a multi-product environment where each buyer has preferences over a d-dimensional variety of goods. The seller is limited to offering a finite number n of d-dimensional choices. The limited menu reflects a finite communication capacity between the buyer and seller. We identify necessary conditions that the optimal finite menu must satisfy, for either the socially efficient or the revenue-maximizing mechanism. These conditions require that information be bundled, or quantized, optimally. We introduce vector quantization and establish that the losses due to finite menus converge to zero at a rate of 1/n(2/d). In the canonical model with one-dimensional products and preferences, this establishes that the loss resulting from using the n-item menu converges to zero at a rate proportional to 1/n(2). (C) 2021 Elsevier Inc. All rights reserved.