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

The article addresses a many-to-one matching problem akin to college admissions, where institutions admit multiple students simultaneously (F1). Unlike traditional models that often assume linear utility functions, this study focuses on non-linear utility functions that incorporate considerations of diversity among students (F2, F3). The authors argue that conventional approaches may be inadequate for achieving stable matchings under these conditions (A1). To overcome these challenges, they propose new solutions grounded in Rawlsian fairness principles, aiming to ensure equitable outcomes in the matching process (F4). The overarching goal is to develop stable matchings that respect both institutional preferences and fairness criteria, particularly when diversity factors influence utility (F5). This approach represents a departure from standard models by explicitly integrating fairness and non-linearity into the matching framework.