Dominant Resource Fairness with Meta-Types

TL;DR

This paper introduces a novel resource allocation mechanism called Dominant Resource Fairness with Meta Types, which handles heterogeneous demands, location constraints, and substitution effects, ensuring fairness and efficiency in complex real-world scenarios.

Contribution

It presents the first study of resource allocation with meta-types, incorporating constraints like location and substitution, and provides a scalable, fair, and strategy-proof solution.

Findings

Mechanism satisfies Pareto optimality, envy-freeness, strategy-proofness.

Method scales better to large problems than alternatives.

Captures real-life constraints more effectively than previous models.

Abstract

Inspired by the recent COVID-19 pandemic, we study a generalization of the multi-resource allocation problem with heterogeneous demands and Leontief utilities. Unlike existing settings, we allow each agent to specify requirements to only accept allocations from a subset of the total supply for each resource. These requirements can take form in location constraints (e.g. A hospital can only accept volunteers who live nearby due to commute limitations). This can also model a type of substitution effect where some agents need 1 unit of resource A \emph{or} B, both belonging to the same meta-type. But some agents specifically want A, and others specifically want B. We propose a new mechanism called Dominant Resource Fairness with Meta Types which determines the allocations by solving a small number of linear programs. The proposed method satisfies Pareto optimality, envy-freeness, strategy-proofness, and a notion of sharing incentive for our setting. To the best of our knowledge, we are the first to study this problem formulation, which improved upon existing work by capturing more constraints that often arise in real life situations. Finally, we show numerically that our method scales better to large problems than alternative approaches.