Optimal selling mechanisms under moment conditions

• 成果类型: Article
• 署名作者: Carrasco, Vinicius; Luz, Vitor Farinha; Kos, Nenad; Messner, Matthias; Monteiro, Paulo; Moreira, Humberto
• 署名单位: Pontificia Universidade Catolica do Rio de Janeiro; University of British Columbia; Bocconi University; Bocconi University; University of Cologne
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2018.05.005
• 发表日期: 2018
• 页码: 245-279
• 关键词: Optimal mechanism design; Robustness; incentive compatibility; individual rationality; ambiguity aversion; moment conditions

摘要

We study the revenue maximization problem of a seller who is partially informed about the distribution of buyer's valuations, only knowing its first N moments. The seller chooses the mechanism generating the best revenue guarantee based on the information available, that is, the optimal mechanism is chosen according to maxmin expected revenue. We show that the transfer function in the optimal mechanism is given by non-negative monotonic hull of a polynomial of degree N. This enables us to transform the seller's problem into a much simpler optimization problem over N variables. The optimal mechanism is found by choosing the coefficients of the polynomial subject to a resource constraint. We show that knowledge of the first moment does not guarantee strictly positive revenue for the seller, characterize the solution for the cases of two moments and derive some characteristics of the solution for the general case. (C) 2018 Published by Elsevier Inc.