When is a monotone function cyclically monotone?

• 成果类型: Article
• 署名作者: Kushnir, Alexey, I; Lokutsievskiy, Lev, V
• 署名单位: Carnegie Mellon University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE4305
• 发表日期: 2021-07-01
• 页码: 853-879
• 关键词: Monotone; cyclically monotone; nonconvex domain; gross substitutes; gross substitutes and complements; mechanism design; algebraic topology; HOMOLOGY; nerve theorem

摘要

We provide sufficient conditions for a monotone function with a finite set of outcomes to be cyclically monotone. Using these conditions, we show that any monotone function defined on the domain of gross substitutes is cyclically monotone. The result also extends to the domain of generalized gross substitutes and complements.