Platform Design in Matching Markets: A Two-Sided Assortment Optimization Approach

Motivated by online dating apps, we consider the assortment optimization problem faced by a two-sided matching platform. Users on each side observe an assortment of profiles and decide which of them to like. A match occurs if and only if two users mutually like each other, potentially in different periods. We study how platforms should make assortment decisions to maximize the expected number of matches under different platform designs, varying (i) how users interact with each other, i.e., whether one or both sides of the market can initiate an interaction, and (ii) the timing of matches, i.e., either sequentially or also simultaneously. We show that the problem is NP-hard and that common approaches perform arbitrarily badly. Given the complexity of the problem and industry practices, we focus on the case with two periods and provide algorithms and performance guarantees for different platform designs. We establish that, when interactions are one-directional and matches only take place sequentially, there is an approximation guarantee of $1-1/e$, which becomes arbitrarily close to $1/2$ if we allow for two-directional interactions. Moreover, when we enable matches to happen sequentially and simultaneously in the first period, we provide an approximation guarantee close to $1/2$, which becomes approximately $1/3$ when we allow two-directional interactions. Finally, we discuss some model extensions and use data from our industry partner to numerically show that the loss for not considering simultaneous matches is negligible. Our results suggest that platforms should focus on simple sequential adaptive policies to make assortment decisions.