Unique stable matchings

Abstract

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 letP⁎be its associated normal form, a (weakly) smaller matching market with the same set of stable matchings that can be obtained using procedures introduced inIrving and Leather (1986)andBalinski and Ratier (1997). The following three statements are equivalent:(a)P has a unique stable matching.(b)Preferences onP⁎are acyclic, as defined byChung (2000).(c)InP⁎every market participant's preference list is a singleton.