  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. 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 (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.
