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.

翻译：我们研究一个多对一匹配问题，例如大学招生问题，其中每所大学可以录取多名学生。与经典模型不同，大学通过非线性效用函数评估学生集合，这些函数能够捕捉学生之间的多样性特征。在此设定下，我们证明经典稳定匹配可能不存在。为解决这一问题，我们提出基于罗尔斯公平的替代解概念，旨在最大化所有大学中的最小效用。我们设计了确定性和随机性算法，通过迭代优化处境最差大学的结果，为稳定性无法保证时的公平分配提供了实用方法。