A note on Kelso and Crawford's gross substitutes condition

• 成果类型: Article
• 署名作者: Fujishige, S; Yang, ZF
• 署名单位: Kyoto University; Yale University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.28.3.463.16393
• 发表日期: 2003
• 页码: 463-469
• 关键词: auction

摘要

In their 1982 article, Kelso and Crawford proposed a gross substitutes condition for the existence of core (and equilibrium) in a two-sided matching model. Since then, this condition has often been used in the literature on matching models and equilibrium models in the presence of indivisibilities. In this paper we prove that a reservation value (or utility) function satisfies the gross substitutes condition if and only if it is an M-#-concave function defined on the unit-hypercube, which is a discrete concave function recently introduced by Murota and Shioura (1999).