Tropical analysis: With an application to indivisible goods

• 成果类型: Article
• 署名作者: Bedard, Nicholas C.; Goeree, Jacob K.
• 署名单位: Wilfrid Laurier University; University of New South Wales Sydney
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE5831
• 发表日期: 2025-07-01
• 页码: 815-829
• 关键词: Conservative correspondences; subgradient theorem; potential theorem; Duality; tropical geometry; convex analysis; normally labeled polyhedral subdivisions; subdifferentials; indivisible goods; C65

摘要

We establish the subgradient theorem for monotone correspondences: a monotone correspondence is equal to the subdifferential of a potential if and only if it is conservative, i.e., its integral along a closed path vanishes irrespective of the selection from the correspondence along the path. We prove two attendant results: the potential theorem, whereby a conservative monotone correspondence can be integrated up to a potential, and the duality theorem, whereby the potential has a dual whose subdifferential is a conservative monotone correspondence that is the inverse of the original correspondence. We use these results to reinterpret and extend Baldwin and Klemperer's (2019) characterization of demand in economies with indivisible goods.