Convexity and multi-dimensional screening for spaces with different dimensions

• 成果类型: Article
• 署名作者: Pass, Brendan
• 署名单位: University of Alberta
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2012.05.004
• 发表日期: 2012
• 页码: 2399-2418
• 关键词: Principal-agent problem; Multi-dimensional screening; monopoly; asymmetric information; convexity; Unequal dimensions; Optimal transportation; exclusion

摘要

We study the principal agent problem. We show that b-convexity of the space of products, a condition which appears in a recent paper by Figalli, Kim and McCann (2011) [9], is necessary to formulate the problem as a maximization over a convex set. We then show that when the dimension m of the space of types is larger than the dimension n of the space of products, this condition implies that the extra dimensions do not encode independent economic information. When m is smaller than n, we show that under b-convexity of the space of types, it is always optimal for the principal to offer goods only from a certain prescribed subset. We show that this is equivalent to offering an m-dimensional space of goods. (C) 2012 Elsevier Inc. All rights reserved.