Matching platforms, such as online dating services and job recommendations, have become increasingly prevalent. For the success of these platforms, it is crucial to design reciprocal recommender systems (RRSs) that not only increase the total number of matches but also avoid creating unfairness among users. In this paper, we investigate the fairness of RRSs on matching platforms. From the perspective of fair division, we define the users' opportunities to be recommended and establish the fairness concept of envy-freeness in the allocation of these opportunities. We first introduce the Social Welfare (SW) method, which approximately maximizes the number of matches, and show that it leads to significant unfairness in recommendation opportunities, illustrating the trade-off between fairness and match rates. To address this challenge, we propose the Nash Social Welfare (NSW) method, which alternately optimizes two NSW functions and achieves nearly envy-free recommendations. We further generalize the SW and NSW method to the $α$-SW method, which balances the trade-off between fairness and high match rates. Additionally, we develop a computationally efficient approximation algorithm for the SW/NSW/$α$-SW methods based on the Sinkhorn algorithm. Through extensive experiments on both synthetic datasets and two real-world datasets, we demonstrate the practical effectiveness of our approach.

翻译：匹配平台，如在线约会服务和职位推荐系统，已变得越来越普遍。为确保这些平台的成功，设计互惠推荐系统至关重要，该系统不仅要增加匹配总数，还要避免在用户间产生不公平。本文研究了匹配平台上互惠推荐系统的公平性问题。从公平分配的角度出发，我们定义了用户的被推荐机会，并建立了这些机会分配中的无嫉妒公平性概念。我们首先介绍了社会福利方法，该方法近似最大化匹配数量，并表明它会导致推荐机会的显著不公平，从而说明了公平性与匹配率之间的权衡。为应对这一挑战，我们提出了纳什社会福利方法，该方法交替优化两个NSW函数，实现近乎无嫉妒的推荐。我们进一步将SW和NSW方法推广为$α$-SW方法，以平衡公平性与高匹配率之间的权衡。此外，基于Sinkhorn算法，我们为SW/NSW/$α$-SW方法开发了一种计算高效的近似算法。通过在合成数据集和两个真实世界数据集上的大量实验，我们证明了所提方法的实际有效性。