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Several resource allocation problems involve multiple types of resources, with a different agency being responsible for "locally" allocating the resources of each type, while a central planner wishes to provide a guarantee on the properties of the final allocation given agents' preferences. We study the relationship between properties of the local mechanisms, each responsible for assigning all of the resources of a designated type, and the properties of a sequential mechanism which is composedarXiv:2101.12522v2 fatcat:gy74wyhkf5cf7h6yy4w44rp2jy