Sequential Mechanisms for Multi-type Resource Allocation [article]

Sujoy Sikdar, Xiaoxi Guo, Haibin Wang, Lirong Xia, Yongzhi Cao
2021 arXiv   pre-print
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 composed
more » ... f these local mechanisms, one for each type, applied sequentially, under lexicographic preferences, a well studied model of preferences over multiple types of resources in artificial intelligence and economics. We show that when preferences are O-legal, meaning that agents share a common importance order on the types, sequential mechanisms satisfy the desirable properties of anonymity, neutrality, non-bossiness, or Pareto-optimality if and only if every local mechanism also satisfies the same property, and they are applied sequentially according to the order O. Our main results are that under O-legal lexicographic preferences, every mechanism satisfying strategyproofness and a combination of these properties must be a sequential composition of local mechanisms that are also strategyproof, and satisfy the same combinations of properties.
arXiv:2101.12522v2 fatcat:gy74wyhkf5cf7h6yy4w44rp2jy