2002 Reports

Random paths to stability in the roommate problem

Diamantoudi, Effrosyni; Miyagawa, Eiichi; Xue, Licun

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.