顺序匹配市场中的多智能体品类优化
Multi-agent Assortment Optimization in Sequential Matching Markets
AI总结：
本文研究双边顺序匹配市场中的多智能体品类优化问题，针对一般选择模型提出 $1-1/e$ 近似算法，并在供应商遵循多项式 logit 模型时突破该近似比，实现渐近最优。
摘要：
在本文中，我们研究由 Ashlagi et al. (2022) 引入的双边顺序匹配模型中的多智能体品类优化问题。该设定如下：我们（平台）向每位顾客提供一个供应商菜单。然后，每位顾客同时且独立地选择与某个供应商匹配或保持未匹配状态。每个供应商观察到选择他们的顾客子集，并选择要么与一位顾客匹配，要么离开系统。因此，只有当顾客和供应商依次相互选择时，匹配才会发生。每个智能体的行为是概率性的，并由离散选择模型决定。我们的目标是选择一个品类族，以最大化匹配的期望收益。鉴于该问题的难度，我们针对异质设定展示了一个 $1-1/e$ 的近似因子，在该设定中顾客遵循一般选择模型，供应商遵循需求函数为单调且次模的一般选择模型。我们的方法足够灵活，可以允许不同的品类约束和收益目标函数。此外，我们设计了一种算法，突破了 $1-1/e$ 的障碍，并且实际上在供应商遵循经典的多项式 logit 选择模型且具有足够选择性时是渐近最优的。最后，我们提供了其他结果和进一步的见解。值得注意的是，在顾客和供应商都遵循多项式 logit 模型的无约束设定中，我们设计了一种简单且高效的近似算法，该算法在一个嵌套品类族上进行适当的随机化。此外，我们分析了匹配市场模型的各个方面，从而得出若干运营见解，例如匹配平台可以从允许更具选择性的智能体发起匹配过程中获益。
英文摘要：
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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