Extreme Points and Majorization: Economic Applications

• 成果类型: Article
• 署名作者: Kleiner, Andreas; Moldovanu, Benny; Strack, Philipp
• 署名单位: Arizona State University; Arizona State University-Tempe; University of Bonn; Yale University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA18312
• 发表日期: 2021
• 页码: 1557-1593
• 关键词: reduced-form auctions; implementation; settings

摘要

We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function f and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of an extreme point in each interval where it is constant. We apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.