A simple decentralized matching mechanism in markets with couples

We analyze a simple decentralized matching mechanism in market with couples called One Application Mechanism. Under this mechanism any stable matching of the market can be attained in Subgame Perfect equilibrium (SPE). In contrast with previous results, we find that the mechanism may attain unstable matchings in SPE. We show that only one special kind of instability is admissible in equilibrium and we argue that this exclusively comes from coordination failures between members of couples. Our main result shows that the One Application Mechanism implements in SPE the set of pairwise stable matchings in markets with couples.