1. 2017) to guarantee the existence of stable outcomes. (Here, by necessary in the maximal domain sense we mean that if one agent's preferences are not substitutable, there exist substitutable preferences for the other agents such that no stable outcome exists. See, e.g., the work of Pycia Pycia;Oviedo Echenique;the setting of many-to-many matching with contracts, substitutable preferences are both sufficient,2017
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