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Research regarding the stable marriage and roommate problem has a long anddistinguished history in mathematics, computer science and economics. Stabilityin this context is predominantly core stability or one of its variants in whicheach deviation is by a group of players. There has been little focus inmatching theory on stability concepts such as Nash stability and individualstability in which the deviation is by a single player. Such stability conceptsare suitable especially when trust for the other party is limited, complexcoordination is not feasible, or when only unmatched agents can be approached.Furthermore, weaker stability notions such as individual stability may inprinciple circumvent the negative existence and computational complexityresults in matching theory. We characterize the computational complexity ofchecking the existence and computing individual-based stable matchings for themarriage and roommate settings. One of our key computational results for thestable marriage setting also carries over to different classes of hedonic gamesfor which individual-based stability has already been of much interest.

Stable marriage and roommate problems with individual-based stability