We study the design of a decentralized two-sided matching market in which agents' search is guided by the platform. There are finitely many agent types, each with (potentially random) preferences drawn from known type-specific distributions. Equipped with such distributional knowledge, the platform guides the search process by determining the meeting rate between each pair of types from the two sides. Focusing on symmetric pairwise preferences in a continuum model, we first characterize the unique stationary equilibrium that arises given a feasible set of meeting rates. We then introduce the platform's optimal directed search problem, which involves optimizing meeting rates to maximize equilibrium social welfare. We first show that incentive issues arising from congestion and cannibalization makes the design problem fairly intricate. Nonetheless, we develop an efficiently computable solution whose corresponding equilibrium achieves at least 1/4 of the optimal social welfare. Our directed search design is simple and easy-to-implement, as its corresponding bipartite graph consists of disjoint stars. Furthermore, our solution implies that the platform can substantially limit choice and yet induce an equilibrium with an approximately optimal welfare. Finally, we show that approximation is the likely best we can hope by establishing that the problem of designing optimal directed search is NP-hard to approximate beyond a certain constant factor.

中文翻译：

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在匹配平台上设计近似最佳搜索

我们研究了一个分散的双向匹配市场的设计，在该市场中，代理商的搜索由该平台指导。代理类型有限，每种类型都有（可能是随机的）从已知的特定于类型的分布中提取的偏好。配备了这种分布知识，该平台通过从两侧确定每对类型之间的会合率来指导搜索过程。关注连续模型中的对称成对偏好，我们首先描述在给定可行的满足率的情况下出现的唯一平稳平衡。然后，我们介绍该平台的最佳定向搜索问题，该问题涉及优化会议率以最大化均衡的社会福利。我们首先表明，由于拥塞和蚕食导致的激励问题使设计问题变得相当复杂。但是，我们开发了一种可计算的解决方案，其相应的平衡至少达到了最佳社会福利的1/4。我们的定向搜索设计简单易实现，因为其对应的二部图由不连续的星组成。此外，我们的解决方案意味着该平台可以实质性地限制选择，但仍可以带来具有最佳福利的平衡。最后，我们通过建立设计最佳有向搜索的问题是NP-难以超出某个恒定因子的NP来证明，近似是我们可能希望的最佳结果。因为其对应的二部图由不连续的星组成。此外，我们的解决方案意味着该平台可以实质性地限制选择，但仍可以带来具有最佳福利的平衡。最后，我们通过证明设计最佳定向搜索的问题是NP-难以超出某个恒定因子的NP来证明，近似是我们可能希望的最佳结果。因为其对应的二分图由不相交的恒星组成。此外，我们的解决方案意味着该平台可以实质性地限制选择，但仍可以带来具有最佳福利的平衡。最后，我们通过建立设计最佳有向搜索的问题是NP-难以超出某个恒定因子的NP来证明，近似是我们可能希望的最佳结果。