Unique stable matchings
研究一对一双边匹配市场中唯一稳定匹配的条件，证明市场具有唯一稳定匹配等价于其规范形式中偏好无环且每个参与者的偏好列表为单元素。
In this paper we consider the issue of a unique prediction in one-to-one two-sided matching markets, as defined by Gale and Shapley (1962), and we prove the following: TheoremLet P be a one-to-one two-sided matching market and let P⁎ be its associated normal form, a (weakly) smaller matching market with the same set of stable matchings that can be obtained using procedures introduced in Irving and Leather (1986) and Balinski and Ratier (1997). The following three statements are equivalent:(a)P has a unique stable matching.(b)Preferences on P⁎ are acyclic, as defined by Chung (2000).(c)In P⁎ every market participant's preference list is a singleton. Theorem Let P be a one-to-one two-sided matching market and let P⁎ be its associated normal form, a (weakly) smaller matching market with the same set of stable matchings that can be obtained using procedures introduced in Irving and Leather (1986) and Balinski and Ratier (1997). The following three statements are equivalent: P has a unique stable matching. Preferences on P⁎ are acyclic, as defined by Chung (2000). In P⁎ every market participant's preference list is a singleton.