This paper studies whether a sequence of myopic blockings leads to a stable matching in the roommate problem. We prove that if a stable matching exists and preferences are strict, then for any unstable matching, there exists a finite sequence of successive myopic blockings leading to a stable matching. This implies that, starting from any unstable matching, the process of allowing a randomly chosen blocking pair to form converges to a stable matching with probability one. This result generalizes those of Roth and Vande Vate (1990) and Chung (2000) under strict preferences. JEL Classification: C62; C71; C78; D71 Keywords: Roommates problem; Marriage problem; Core convergence; Indirect domination; Cycle; Odd ring * We thank Alvin Roth for pointing out a false statement in the previous version, John Vande Vate for detailed suggestions, Hideo Konishi for helpful conversations, and anonymous referees for helpful comments and suggestions.
If the no-odd-ring condition is not satisfied but preferences are strict and stable matchings exist then the Roth and Vande Vate path still converges to a stable matching REF ).
Random paths to stability in the roommate problem
Games and Economic Behavior
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