平衡匹配数量与双方推荐公平性，提升婚恋平台匹配效率

Recommender systems play an increasingly crucial role in shaping people's opportunities, particularly in online dating platforms. It is essential from the user's perspective to increase the probability of matching with a suitable partner while ensuring an appropriate level of fairness in the matching opportunities. We investigate reciprocal recommendation in two-sided matching markets between agents divided into two sides. In our model, a match is considered successful only when both individuals express interest in each other. Additionally, we assume that agents prefer to appear prominently in the recommendation lists presented to those on the other side. We define each agent's opportunity to be recommended and introduce its fairness criterion, envy-freeness, from the perspective of fair division theory. The recommendations that approximately maximize the expected number of matches, empirically obtained by heuristic algorithms, are likely to result in significant unfairness of opportunity. Therefore, there can be a trade-off between maximizing the expected matches and ensuring fairness of opportunity. To address this challenge, we propose a method to find a policy that is close to being envy-free by leveraging the Nash social welfare function. Experiments on synthetic and real-world datasets demonstrate the effectiveness of our approach in achieving both relatively high expected matches and fairness for opportunities of both sides in reciprocal recommender systems.