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I know that in a marriage problem for example, you may have more than one stable allocations but I think that the Gale-Shapley algorithm just provide only one.

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  • $\begingroup$ In the usual setting with strict preferences, there is one for each proposing side. These two allocations coincide if and only if there is a unique stable matching. $\endgroup$ May 29, 2023 at 14:00

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