Motivated by the challenges faced by choice-based matching platforms, in this work, we study a generalization of the foundational model introduced by Ashlagi et al. (2022). Specifically, this model consists of two sides (e.g., customers and suppliers) who have preferences over the opposite side in the form of discrete choice models. A matching is realized through a two-step process where the platform's decision is to initially present to each agent on one side an assortment of users of the opposite side. The ultimate goal of the platform is to maximize the total expected revenue collected from the matching. Due to the computational complexity of this problem, we focus on the design of approximation algorithms with constant-factor guarantees for the constrained version of the problem under general choice preferences. First, to the best of our knowledge, we are the first to draw connections with the literature of submodular optimization and show that one-sided choice-oblivious approaches perform arbitrarily bad. Second, we show that, for the general setting, there exists a two-sided choice-aware randomized algorithm that achieves a (1-1/e)-approximation factor, which is the best possible. Third, we design an algorithm that is asymptotically optimal when one side follows the well-known multinomial-logit (MNL) choice model under the small probability regime. Fourth, we provide a simple and effective algorithm with a 1/4-approximation guarantee for the unconstrained setting with both sides following MNL models. Finally, we assess the performance of our proposed methods with a detailed computational study and discuss several extensions.

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