Semi-stability in roommate problems

P. Jean-Jacques Herings and Yu Zhou ()
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Yu Zhou: Department of Economics, Graduate School of Economics, Nagoya University

Theoretical Economics, Forthcoming

Abstract: 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 semi-stability by showing its equivalence to a newly proposed choice-based equilibrium concept. We show that undominated semi-stable outcomes are Pareto optimal and under strict preferences, every semi-stable outcome is Pareto optimal. Nevertheless, standard structural properties, such as the rural hospital theorem and the lattice properties, fail for semi-stable outcomes. We also discuss possible applications.

Keywords: Roommate problem; semi-stability; choice-based equilibrium; Pareto optimality (search for similar items in EconPapers)
JEL-codes: C72 C78 D47 (search for similar items in EconPapers)
Date: 2026-07-06
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