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In a many-to-one matchingmodel with responsive preferences in whichindifferences are allowed, we study three notions of core, three notions ofstability, and their relationships. We show that (i) the core contains thestable set, (ii) the strong core coincides with the strongly stable set, and(iii) the super core coincides with the super stable set. We also show how thecore and the strong core in markets with indifferences relate to the stablematchings of their associated tie-breaking strict markets.

Core and stability notions in many-to-one matching markets with indifferences