Two-sided platforms rely on their recommendation algorithms to help visitors successfully find a match. However, on platforms such as VolunteerMatch (VM) -- which has facilitated millions of connections between volunteers and nonprofits -- a sizable fraction of website traffic arrives directly to a nonprofit's volunteering page via an external link, thus bypassing the platform's recommendation algorithm. We study how such platforms should account for this external traffic in the design of their recommendation algorithms, given the goal of maximizing successful matches. We model the platform's problem as a special case of online matching, where (using VM terminology) volunteers arrive sequentially and probabilistically match with one opportunity, each of which has finite need for volunteers. In our framework, external traffic is interested only in their targeted opportunity; by contrast, internal traffic may be interested in many opportunities, and the platform's online algorithm selects which opportunity to recommend. In evaluating different algorithms, we parameterize the competitive ratio based on the amount of external traffic. After demonstrating the shortcomings of a commonly-used algorithm that is optimal in the absence of external traffic, we propose a new algorithm -- Adaptive Capacity (AC) -- which accounts for matches differently based on whether they originate from internal or external traffic. We provide a lower bound on AC's competitive ratio that is increasing in the amount of external traffic and that is close to (and, in some regimes, exactly matches) the parameterized upper bound we establish on the competitive ratio of any online algorithm. We complement our theoretical results with a numerical study motivated by VM data that demonstrates the strong performance of AC and furthers our understanding of the difference between AC and other commonly-used algorithms.

翻译：双边平台依赖其推荐算法帮助访问者成功完成匹配。然而，在像VolunteerMatch（VM）这样的平台（该平台已促成数百万志愿者与公益组织之间的连接）上，相当一部分网站流量通过外部链接直接到达公益组织的志愿服务页面，从而绕过了平台的推荐算法。我们研究了这类平台在以实现成功匹配最大化为目标的设计推荐算法时，应如何考虑这种外部流量。我们将平台问题建模为在线匹配的一种特殊情形，其中（沿用VM术语）志愿者按序到达并与一个机会实现概率性匹配，每个机会对志愿者有有限需求。在我们的框架中，外部流量仅对其目标机会感兴趣；相比之下，内部流量可能对多个机会感兴趣，而平台在线算法则选择推荐哪个机会。在评估不同算法时，我们根据外部流量比例参数化竞争比。在论证了在没有外部流量时最优的常用算法存在缺陷后，我们提出一种新算法——自适应容量（AC）——该算法根据匹配源于内部还是外部流量而采取不同的处理方式。我们给出了AC算法竞争比的下界，该下界随外部流量增加而提升，并且接近（在某些情况下完全匹配）我们为任意在线算法竞争比建立的参数化上界。我们通过基于VM数据的数值研究对理论结果进行补充，该研究证明了AC算法的优越性能，并加深了我们对AC与其他常用算法差异的理解。