Optimal multi-unit mechanisms with private demands

• 成果类型: Article
• 署名作者: Devanur, Nikhil R.; Haghpanah, Nima; Psomas, Alexandros
• 署名单位: Amazon.com; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Alphabet Inc.; Google Incorporated
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2020.03.007
• 发表日期: 2020
• 页码: 482-505
• 关键词: Mechanism design; Multi-unit demands; deterministic mechanisms

摘要

A seller can produce multiple units of a single good. The buyer has constant marginal value for each unit she receives up to a demand, and zero marginal value for units beyond the demand. The marginal value and the demand are drawn from a distribution and are privately known to the buyer. We show that under natural regularity conditions on the distribution, the optimal (revenue-maximizing) selling mechanism is deterministic. It is a price schedule that specifies the payment based on the number of units purchased. Further, under the same conditions, the revenue as a function of the price schedule is concave, which in turn implies that the optimal price schedule can be found in polynomial time. We give a more detailed characterization of the optimal prices when there are only two possible demands. (C) 2020 Elsevier Inc. All rights reserved.