On the Lattice Structure of Stable Allocations in a Two-Sided Discrete-Concave Market

• 成果类型: Article
• 署名作者: Murota, Kazuo; Yokoi, Yu
• 署名单位: University of Tokyo
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0679
• 发表日期: 2015
• 页码: 460-473
• 关键词: m-convex; gross substitutes; equilibrium; matchings; STABILITY

摘要

The stable allocation model is a many-to-many matching model in which each pair's partnership is represented by a nonnegative integer. This paper establishes a link between two different formulations of this model: the choice function model studied thoroughly by Alkan and Gale and the discrete-concave (M-concave) value function model introduced by Eguchi, Fujishige, and Tamura. We show that the choice functions induced from M-concave value functions are endowed with consistency, persistence, and size monotonicity. This implies, by the result of Alkan and Gale, that the stable allocations for M-concave value functions form a distributive lattice with several significant properties such as polarity, complementarity, and uni-size property. Furthermore, we point out that these results can be extended for quasi M-concave value functions.