Sequential Mechanisms for Multi-type Resource Allocation

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 of 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.

Authors

• Sujoy Sikdar
• Xiaoxi Guo Ant Group
• Haibin Wang
• Lirong Xia Rensselaer Polytechnic Institute
• Yongzhi Cao Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education, School of Computer Science, Peking University, Beijing, China

Keywords

• Multi-type resource Allocation
• Sequential Mechanisms
• Computational Social Choice
• Mechanism Design