公平稳定匹配：一种纳什社会福利方法

中文摘要 AI 辅助

传统稳定匹配算法（如Gale-Shapley算法）优先考虑稳定性，但可能无法实现参与者之间的公平结果。我们研究纳什社会福利（NSW）作为经典稳定婚姻问题中公平目标的作用，开发了SNSW-Alg算法，该算法在秩诱导效用下寻找最大化纳什社会福利的稳定匹配，时间复杂度为$\tilde{\text{O}}(n^4)$，其中$n$为男性或女性的数量。我们证明SNSW-Alg在保持稳定性的同时平衡了公平性，在不同偏好分布下对方法进行实证评估，结果显示在公平性上有显著提升，而在遗憾、平均主义准则和性别平等等其他关键指标上没有大幅损失。我们的研究发现，基于其他公平指标（遗憾、平均主义、性别平等）的稳定匹配，SNSW-Alg生成的稳定匹配在统计上是帕累托非支配的，本研究为设计公平稳定匹配提供了重要见解。

英文摘要

While traditional stable matching algorithms, such as the Gale-Shapley algorithm, prioritize stability, they may fall short of achieving equitable outcomes among participants. We study the role of \emph{Nash social welfare} (NSW) as a fairness objective in the classic \emph{stable marriage problem}. We develop \texttt{SNSW-Alg} that finds a stable matching that maximizes Nash social welfare under rank-induced utilities in $\tilde{\mathcal{O}}(n^4)$ time, where $n$ is the number of men or women. We demonstrate that \texttt{SNSW-Alg} balances equity while preserving stability. We empirically evaluate our methods across diverse preference distributions, demonstrating significant gains in fairness without substantial losses in other key measures such as regret, egalitarian criterion, and sex equality. Our findings suggest that the stable matching produced by \texttt{SNSW-Alg} is statistically Pareto-undominated by stable matchings based on other fairness measures - regret, egalitarian, and sex equality. This study offers compelling insights for designing fair-stable matching.

发表机构

• IIIT Hyderabad（印度信息技术与管理大学海得拉巴分校）
• IIT Hyderabad（印度理工学院海得拉巴分校）

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