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@@ -42,6 +42,3 @@ Gale-Shapley algorithm implies a centralized authority who can match men and wom
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**Question:** Can a group of men and women reach a stable outcome if they match up in a decentralized way? In other words, if men and women date each other, break up, date another, break up, etc. out on their own, can they reach a stable matching eventually?
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Roth and van de Vate (1990) answered this question in the affirmative. They proved that starting from any unstable matching, there exists a path to *a* stable matching. This result suggests that stable matchings are a natural converging point for two-sided matching problems. Note that we are not sure which stable matching will be reached in this decentralized setting, whereas in the Gale-Shapley algorithm, we are very certain which stable matching will be reached.
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