Near-feasible Fair Allocations in Two-sided Markets

TL;DR

This paper introduces a flexible framework for resource allocation in two-sided markets that balances fairness and feasibility, using iterative rounding to achieve near-feasible solutions with guarantees across various market design problems.

Contribution

It presents a novel general modeling and algorithmic framework for near-feasible fair allocations, applicable to diverse two-sided market problems.

Findings

Existence of near-feasible allocations with adjustable fairness trade-offs

A simple sufficient condition for successful rounding to integer allocations

Strengthened guarantees for fairness notions in three market design problems

Abstract

We study resource allocation in two-sided markets from a fundamental perspective and introduce a general modeling and algorithmic framework to effectively incorporate the complex and multidimensional aspects of fairness. Our main technical contribution is to show the existence of a range of near-feasible resource allocations parameterized in different model primitives to give flexibility when balancing the different policymaking requirements, allowing policy designers to fix these values according to the specific application. To construct our near-feasible allocations, we start from a fractional resource allocation and perform an iterative rounding procedure to get an integer allocation. We show a simple yet flexible and strong sufficient condition for the target feasibility deviations to guarantee that the rounding procedure succeeds, exhibiting the underlying trade-offs between market capacities, agents' demand, and fairness. To showcase our framework's modeling and algorithmic capabilities, we consider three prominent market design problems: school allocation, stable matching with couples, and political apportionment. In each of them, we obtain strengthened guarantees on the existence of near-feasible allocations capturing the corresponding fairness notions, such as proportionality, envy-freeness, and stability.