The primary contribution of this paper resides in devising constant-factor approximation guarantees for revenue maximization in two-sided matching markets, under general pairwise rewards. A major distinction between our work and state-of-the-art results in this context (Ashlagi et al., 2022; Torrico et al., 2023) is that, for the first time, we are able to address reward maximization, reflected by assigning each customer-supplier pair an arbitrarily-valued reward. The specific type of performance guarantees we attain depends on whether one considers the customized model or the inclusive model. The fundamental difference between these settings lies in whether the platform should display to each supplier all selecting customers, as in the inclusive model, or whether the platform can further personalize this set, as in the customized model. Technically speaking, our algorithmic approach and its analysis revolve around presenting novel linear relaxations, leveraging convex stochastic orders, employing approximate dynamic programming, and developing tailor-made analytical ideas. In both models considered, these ingredients allow us to overcome the lack of submodularity and subadditivity that stems from pairwise rewards, plaguing the applicability of existing methods.

翻译：本文的主要贡献在于为双边匹配市场中的收益最大化问题设计了常数因子近似保证，该问题考虑了通用的成对奖励机制。我们的工作与此领域的最新研究成果（Ashlagi等人，2022；Torrico等人，2023）的一个关键区别在于，我们首次能够处理奖励最大化问题，其体现方式是为每个客户-供应商对分配任意取值的奖励。我们所获得的性能保证的具体类型取决于所考虑的模型是定制化模型还是包容性模型。这两种设置的根本差异在于：平台是否应向每个供应商展示所有选择该供应商的客户（如包容性模型），或者平台是否可以进一步个性化定制该展示集合（如定制化模型）。从技术角度而言，我们的算法方法及其分析围绕以下几个方面展开：提出新颖的线性松弛方法、利用凸随机序、采用近似动态规划以及发展定制化的分析思想。在所考虑的两种模型中，这些技术要素使我们能够克服因成对奖励机制导致的子模性和次可加性缺失问题，该问题一直困扰着现有方法的适用性。