Fair Resource Allocation for Demands with Sharp Lower Tail Inequalities

TL;DR

This paper studies fair resource allocation among groups with demands satisfying sharp lower tail inequalities, demonstrating that proportional allocation is nearly optimal and fair, with minimal efficiency loss when slight unfairness is permitted.

Contribution

It introduces a natural proportional allocation method for demands with sharp lower tail inequalities and proves its near fairness and efficiency, extending prior models.

Findings

Proportional allocation performs well for demand distributions with sharp lower tail inequalities.

The allocation achieves near-maximal utilization and fairness.

Allowing small unfairness results in a Price of Fairness close to 1.

Abstract

We consider a fairness problem in resource allocation where multiple groups demand resources from a common source with the total fixed amount. The general model was introduced by Elzayn et al. [FAT*'19]. We follow Donahue and Kleinberg [FAT*'20] who considered the case when the demand distribution is known. We show that for many common demand distributions that satisfy sharp lower tail inequalities, a natural allocation that provides resources proportional to each group's average demand performs very well. More specifically, this natural allocation is approximately fair and efficient (i.e., it provides near maximum utilization). We also show that, when small amount of unfairness is allowed, the Price of Fairness (PoF), in this case, is close to 1.