To address the challenge of choice congestion in matching markets, in this work, we introduce a two-sided assortment optimization framework under general choice preferences. The goal in this problem is to maximize the expected number of matches by deciding which assortments are displayed to the agents and the order in which they are shown. In this context, we identify several classes of policies that platforms can use in their design. Our goals are: (1) to measure the value that one class of policies has over another one, and (2) to approximately solve the optimization problem itself for a given class. For (1), we define the adaptivity gap as the worst-case ratio between the optimal values of two different policy classes. First, we show that the gap between the class of policies that statically show assortments to one-side first and the class of policies that adaptively show assortments to one-side first is exactly $1-1/e$. Second, we show that the gap between the latter class of policies and the fully adaptive class of policies that show assortments to agents one by one is exactly $1/2$. We also note that the worst policies are those who simultaneously show assortments to all the agents, in fact, we show that their adaptivity gap even with respect to one-sided static policies can be arbitrarily small. For (2), we first show that there exists a polynomial time policy that achieves a $1/4$ approximation factor within the class of policies that adaptively show assortments to agents one by one. Finally, when agents' preferences are governed by multinomial-logit models, we show that a 0.066 approximation factor can be obtained within the class of policies that show assortments to all agents at once.

翻译：为解决匹配市场中选择拥堵的挑战，本文在一般选择偏好下引入双边品种组合优化框架。该问题的目标是通过决定向代理展示哪些品种组合及其展示顺序来最大化预期匹配数量。在此背景下，我们识别出平台在设计时可使用的多类策略。我们的目标是：(1) 衡量一类策略相对于另一类策略的价值，以及(2) 针对给定策略类近似求解优化问题本身。对于(1)，我们将自适应差距定义为两类不同策略最优值之间的最坏情况比率。首先，我们证明静态向单侧优先展示品种组合的策略类与自适应向单侧优先展示品种组合的策略类之间的差距恰好为$1-1/e$。其次，我们证明后一类策略与逐个自适应向代理展示品种组合的完全自适应策略类之间的差距恰好为$1/2$。我们还注意到最差的策略是同时向所有代理展示品种组合的策略，事实上，我们证明此类策略相对于单侧静态策略的自适应差距可以任意小。对于(2)，我们首先证明在逐个自适应向代理展示品种组合的策略类中存在一个多项式时间策略，可实现$1/4$的近似因子。最后，当代理偏好服从多项逻辑模型时，我们证明在一次性向所有代理展示品种组合的策略类中可获得0.066的近似因子。