# Sequential Mechanisms for Multi-type Resource Allocation

arXiv: https://arxiv.org/abs/2101.12522 · HTML: https://mlsanity.com/paper/2101.12522/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 37 references that are in the map.
- First posted on arXiv 29 Jan 2021.

## Builds on (most cited first, 4 of 4)

- [Allocating Indivisible Items in Categorized Domains](https://mlsanity.com/paper/1504.05932/) (2015)
- [Multi-type Resource Allocation with Partial Preferences](https://mlsanity.com/paper/1906.06836/) (2019)
- [Mechanism Design for Multi-Type Housing Markets](https://mlsanity.com/paper/1611.07636/) (2016)
- [Probabilistic Serial Mechanism for Multi-Type Resource Allocation](https://mlsanity.com/paper/2004.12062/) (2020)

## Abstract (arXiv)

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.