This paper studies the one-to-one two-sided marriage model (Gale and Shapley 1962). If agents’ preferences exhibit mutually best (i.e., each agent is most preferred by her/his most preferred matching partner), there is a unique stable matching without rank gaps (i.e., in each matched pair the agents assign one another the same rank). We study in how far this result is robust for matching markets that are “close” to mutually best. Without a restriction on preference profiles, we find that natural “distances” to mutually best neither bound the size of the core nor the rank gaps at stable matchings. However, for matching markets that satisfy horizontal heterogeneity, “local” distances to mutually best provide bounds for the size of the core and the rank gaps at stable matchings.

本文研究了一对一的双面婚姻模型（Gale和Shapley 1962）。如果座席的偏好表现出最佳的相互偏好（即，每个座席最受其最喜欢的匹配伙伴的青睐），则存在唯一的稳定匹配而没有等级差距（即，在每个匹配对中，座席彼此分配相同的等级） 。我们研究了这种结果在匹配“接近”互惠的市场方面有多强。在没有偏好配置文件的限制的情况下，我们发现，相互之间最佳的自然“距离”既不会限制核心的大小，也不会限制稳定匹配时的排名差距。但是，对于满足水平异质性的匹配市场，在最佳匹配条件下，相互之间最佳的“局部”距离为核心的大小和等级差距提供了界限。