Stochastic Stability for Roommate Markets

We show that for any roommate market the set of stochastically stable matchings coincideswith the set of absorbing matchings. This implies that whenever the core is non-empty (e.g.,for marriage markets), a matching is in the core if and only if it is stochastically stable, i.e., stochastic stability is a characteristic of the core. Several solution concepts have beenproposed to extend the core to all roommate markets (including those with an empty core).An important implication of our results is that the set of absorbing matchings is the onlysolution concept that is core consistent and shares the stochastic stability characteristic withthe core.