多对一稳定匹配的格结构

Lattice Structure of Many-to-one Stable Matchings

在双方市场中定义的博弈概念,可以使市场同方参与者的收益同时达到最大.这种最优化存在的理论依据是选择匹配的稳定性,选择匹配的稳定性赋予稳定匹配集合一定的格结构,稳定匹配集合的格结构给出了达到最优化的具体路径.本文用博弈论的分析与证明方法研究多对一双方匹配市场中的优化路径,证明稳定匹配集合在Blair偏序下是一个满足分配律的完备格.

The game-theoretic solutions defined in two-sided market allow the interests of agents on the same side of the market to be simultaneously maximized. The theoretic basis of such kind of optimization is the stability of the selection matchings, the stability of the selection matchings endows the set of stable matchings a lattice structure, and the lattice structure of the stable matchings give paths to the optimal outcomes. This paper uses game-theoretic method to study the optimal-path in many-to-one two-sided matching market, we prove that the set of stable matchings is a complete distributive lattice under Blair＇s partial order.