Credible Stability in the Roommate Problem

In the roommate problem, it is known that a stable matching may not exist. In this paper, we propose a new deviation-proof concept, called credible stability, and show that the concept resolves the problem. At a credibly stable matching, any coalition which deviates from the matching is punishable; a deviating coalition is punishable if there exists a further deviation that makes some agent in the firstly moved coalition weakly worse off compared with the initial matching. We show that there always exists a weakly Pareto efficient credibly setwise stable matching in the roommate problem. Moreover, we show that in some cases the credible stability concept assigns an agent who is single at any stable matchings to another agent in the marriage problem. That is, the credible stability overcomes the wellknown rural hospital theorem which is one of the most serious drawbacks of the stable matchings. However, as a negative result, we present the impossibility theorem for strategy-proof credibly pairwise stable matching mechanism.