Semistability in roommate problems

We study the roommate problem allowing for preferences with indifferences and agents remaining single. A stable outcome need not exist. We introduce semi‐stability, a novel notion that guarantees existence and restores stability through minimal policy or group interventions. We build an equilibrium foundation for semistability by showing its equivalence to a newly proposed choice‐based equilibrium concept. We show that undominated semistable outcomes are Pareto optimal and under strict preferences, every semistable outcome is Pareto optimal. Nevertheless, standard structural properties, such as the rural hospital theorem and the lattice properties, fail for semistable outcomes. We also discuss possible applications.