Rawlsian many-to-one matching with non-linear utility

TL;DR

This paper explores a many-to-one matching problem with non-linear utilities, introducing Rawlsian fairness concepts and algorithms to ensure equitable college admissions when classical stability is unattainable.

Contribution

It proposes new fairness-based solution concepts and algorithms for non-linear utility matching problems where classical stability may not exist.

Findings

Classical stable matchings may not exist with non-linear utilities.

Rawlsian fairness can be used to improve fairness in such matchings.

Algorithms can iteratively enhance the worst-off college's utility.

Abstract

We study a many-to-one matching problem, such as the college admission problem, where each college can admit multiple students. Unlike classical models, colleges evaluate sets of students through non-linear utility functions that capture diversity between them. In this setting, we show that classical stable matchings may fail to exist. To address this, we propose alternative solution concepts based on Rawlsian fairness, aiming to maximize the minimum utility across colleges. We design both deterministic and stochastic algorithms that iteratively improve the outcome of the worst-off college, offering a practical approach to fair allocation when stability cannot be guaranteed.