simple, 𝑂(𝑛2)algorithm to compute a stable matching corollary a stable matching always exists. The “stable roommates problem” doesn’t always have. There exists stable matching s in which a is paired with a man, say y, whom she likes less than z. while the mating ritual produces one stable matching, stable matchings need not be unique. For example, reversing the roles of men and women will often yield a different. even worse, in order to use a centralized matching algorithm, you must convince thousands of residency programs to list their positions…