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 0.082 approximation factor can be obtained within the class of policies that show assortments to all agents at once.

翻译：为解决匹配市场中的选择拥堵挑战，本文引入了一个基于一般选择偏好的双边选品优化框架。该问题的目标是通过决定向代理人展示哪些选品及其展示顺序，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采用的几类策略。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该优化问题本身。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，我们证明静态单边优先展示选品的策略类与自适应单边优先展示选品的策略类之间的差距恰好为$1-1/e$。其次，我们证明后者与逐一向代理人自适应展示选品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，最差的策略是那些同时向所有代理人展示选品的策略，事实上，我们证明其相对于单边静态策略的自适应差距可以任意小。对于(2)，我们首先证明在逐一向代理人自适应展示选品的策略类中存在一个达到$1/4$近似比的多项式时间策略。最后，当代理人偏好受多项逻辑模型支配时，我们证明在同时向所有代理人展示选品的策略类中可以获得0.082的近似比。