Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies whether a sequence of myopic blockings leads to a stable matching in the roommate problem.  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 [Econometrica 58 (1990) 1475] and Chung [Games Econ. Behav. 33 (2000) 206] under strict preferences.
['Effrosyni Diamantoudi', 'Eiichi Miyagawa', 'Licun Xue']
I am writing a research paper on a idea Random Paths to Stability in the Roommate Problem
[{"from": "human", "value": "I am writing a research paper on a idea Random Paths to Stability in the Roommate Problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies whether a sequence of myopic blockings leads to a stable matching in the roommate problem.  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 [Econometrica 58 (1990) 1475] and Chung [Games Econ. Behav. 33 (2000) 206] under strict preferences."}]