Unique Stable Matchings

Abstract

We provide necessary and sufficient conditions on the preferences of market participants for a unique stable matching in models of twosided matching with non-transferable utility. We use the process of iterated deletion of unattractive alternatives (IDUA), a formalisation of the reduction procedure in Balinski and Ratier (1997), and we show that an instance of the matching problem possesses a unique stable matching if and only if IDUA collapses each participant's preference list to a singleton. (This is in a sense the matching problem analog of a strategic game being 'dominance solvable'.

Preference swaps for the stable matching problem

“…Maffray [13] gave another representation of SMP using directed graphs, which does not use explicit preference lists. Maffray's representation is better suitable for some SMP studies than the standard one [1,2,10]. Our new representation of SMP uses extended bipartite graphs and no preference lists either.…”