Technical Note—Assortment Planning for Two-Sided Sequential Matching Markets

Abstract

Two-sided platforms, which enable two distinct groups of agents to match and transact with each other, are now ubiquitous in a variety of markets, such as those for labor, dating, and accommodation rentals. Many such online platforms, rather than determining who matches with whom in a centralized fashion, operate by presenting users with a set of recommended partners and allowing them to choose which of these to pursue a match with. Therefore, a question that is central to the operations of these platforms is how to optimize over the recommendations for potential partners that are presented to their users. A natural objective in many markets is to maximize the total number of transactions matches (e.g., the number of tasks completed) that occur through the platform. The platform must account for the fact that a match between two users occurs only when both users find each other acceptable and that when many conflicting requests are received at the same time, not all such requests can be accepted. To describe the tradeoff that then arises, let us refer to the two sides of the market as customers and suppliers, respectively, where we assume that customers (potential guests or clients) are presented with recommended assortments of potential suppliers (properties or freelancers) from which to choose. Naturally, increasing the number and mix of potential suppliers that a customer sees increases the chances that she finds an acceptable one to contact, instead of choosing not to pursue a match through the platform at all. However, if, as a result, the same supplier is shown to many customers, this would increase the chances that a supplier is contacted by many customers with conflicting requests at the same time, resulting in collisions when only one such request can be accepted. In a setting where suppliers are indeed products and do not have preferences, these collisions are bad for the platform, as the number of transactions could have been increased by redirecting some of these customers to other products. However, in a two-sided market, having a supplier receiving many requests might indeed increase the number of matches, as this may increase the chances she finds a customer she prefers to her outside option. Motivated by the above discussion, we study how to optimize over the assortments of recommended potential partners that are shown to each user to maximize the number of matches. Our contributions are twofold: We propose a novel stylized model that captures the aforementioned tradeoffs, and we construct a simple algorithm that achieves a constant-factor approximation to the optimal number of matches.