Abstract
Motivated by online labor markets, we consider the online assortment optimization problem faced by a two-sided matching platform that hosts a set of suppliers waiting to match with a customer. Arriving customers are shown an assortment of suppliers, and may choose to issue a match request to one of them. After spending some time on the platform, each supplier reviews all the match requests he has received and, based on his preferences, he chooses whether to match with a customer or to leave unmatched. We study how platforms should design online assortment algorithms to maximize the expected number of matches in such two-sided settings. We show that, when suppliers do not immediately accept/reject match requests, our problem is fundamentally different from the standard (one-sided) assortment problem, where customers choose over a set of products. We establish that a simple greedy algorithm is 1/2-competitive against an optimal clairvoyant algorithm that knows in advance the full sequence of customers' arrivals. However, unlike related online assortment problems, no randomized algorithm can achieve a better competitive ratio, even in asymptotic regimes. To advance beyond this general impossibility, we consider structured settings where suppliers' preferences are described by the Multinomial Logit and Nested Logit choice models. We develop specialized balancing algorithms, which we call preference-aware, that leverage general information about the suppliers' choice models. In certain settings, the resulting competitive ratios are provably larger than the standard "barrier" of 1-1/e in the adversarial arrival model. Overall, our results suggest that the shape and timing of suppliers' preferences play critical roles in designing online two-sided assortment algorithms.