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.

翻译：本文研究了Ashlagi等人（2022）提出的双边序列匹配模型中多智能体产品组合优化问题。设定如下：平台为每位顾客提供一组供应商菜单。每位顾客同时且独立地选择与某供应商匹配或保持未匹配状态。每位供应商观察到选择自己的顾客子集后，选择与某顾客匹配或离开系统。因此，只有当顾客与供应商依次相互选择时，匹配才会发生。每个智能体的行为具有概率性，并由离散选择模型决定。我们的目标是选择能够最大化匹配预期收益的产品组合族。鉴于该问题的难度，针对顾客遵循一般选择模型、供应商遵循需求函数单调且子模的一般选择模型的异质场景，我们证明了$1-1/e$的近似比。该方法足够灵活，可适用于不同类型的产品组合约束及收益目标函数。此外，我们设计了一种打破$1-1/e$界限的算法，且当供应商遵循经典多项式逻辑选择模型并具有足够选择性时，该算法实际上是渐近最优的。最后，我们提供了其他结果与更深入的见解。值得注意的是，在顾客与供应商均遵循多项式逻辑模型的无约束场景下，我们设计了一种简单高效的近似算法，该算法通过对嵌套产品组合族进行适当随机化来运作。同时，我们分析了匹配市场模型的多个方面，得到若干运营启示，例如匹配平台可通过允许更具选择性的智能体发起匹配过程而获益。