Sequential Mechanisms for Multi-type Resource Allocation

TL;DR

This paper investigates how local resource allocation mechanisms can be combined sequentially to form a global mechanism that preserves desirable properties like strategyproofness and Pareto-optimality under lexicographic preferences.

Contribution

It establishes conditions under which properties of local mechanisms are preserved in the sequential composition for multi-type resource allocation with lexicographic preferences.

Findings

Sequential mechanisms inherit properties from local mechanisms when preferences are O-legal.

Strategyproofness and other properties are maintained in the global mechanism if local mechanisms satisfy them.

Under O-legal lexicographic preferences, all strategyproof mechanisms are sequential compositions of local strategyproof mechanisms.

Abstract

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.