Multi-agent Assortment Optimization in Sequential Matching Markets

In this work, we study the multi-agent assortment optimization problem in the two-sided sequential matching model introduced by Ashlagi et al. (2022). The setting is the following: we (the platform) offer a menu of suppliers to each customer. Then, every customer selects, simultaneously and independently, to match with a supplier or to remain unmatched. Each supplier observes the subset of customers that selected them, and choose either to match a customer or to leave the system. Therefore, a match takes place if both a customer and a supplier sequentially select each other. Each agent's behavior is probabilistic and determined by a discrete choice model. Our goal is to choose an assortment family that maximizes the expected revenue of the matching. Given the hardness of the problem, we show a $1-1/e$-approximation factor for the heterogeneous setting where customers follow general choice models and suppliers follow a general choice model whose demand function is monotone and submodular. Our approach is flexible enough to allow for different assortment constraints and for a revenue objective function. Furthermore, we design an algorithm that beats the $1-1/e$ barrier and, in fact, is asymptotically optimal when suppliers follow the classic multinomial-logit choice model and are sufficiently selective. We finally provide other results and further insights. Notably, in the unconstrained setting where customers and suppliers follow multinomial-logit models, we design a simple and efficient approximation algorithm that appropriately randomizes over a family of nested-assortments. Also, we analyze various aspects of the matching market model that lead to several operational insights, such as the fact that matching platforms can benefit from allowing the more selective agents to initiate the matchmaking process.