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Consider a variant of stable matching in which at every point, either a free college or a free student can propose. As in the Gale-Shapley algorithm, proposals are done going down in the preference list, so that a proposer cannot repeat a proposal to the same partner. Show that this algorithm always terminates with a perfect matching, but not necessarily a stable one.1

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Consider a variant of stable matching in which at every point, either a free college or a free stude...

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