We address the challenging problem of dynamically pricing complementary items that are sequentially displayed to customers. An illustrative example is the online sale of flight tickets, where customers navigate through multiple web pages. Initially, they view the ticket cost, followed by ancillary expenses such as insurance and additional luggage fees. Coherent pricing policies for complementary items are essential because optimizing the pricing of each item individually is ineffective. Our scenario also involves a sales constraint, which specifies a minimum number of items to sell, and uncertainty regarding customer demand curves. To tackle this problem, we originally formulate it as a Markov Decision Process with constraints. Leveraging online learning tools, we design a primal-dual online optimization algorithm. We empirically evaluate our approach using synthetic settings randomly generated from real-world data, covering various configurations from stationary to non-stationary, and compare its performance in terms of constraints violation and regret against well-known baselines optimizing each state singularly.

翻译：我们研究了针对顺序展示给客户的互补商品进行动态定价这一具有挑战性的问题。一个典型的例子是在线机票销售，客户会浏览多个网页：首先看到机票价格，随后是保险和额外行李费等附加费用。为互补商品制定连贯的定价策略至关重要，因为单独优化每件商品的价格是无效的。我们的场景还涉及销售约束（即规定最低销售数量）以及客户需求曲线的不确定性。为解决此问题，我们首次将其建模为一个带约束的马尔可夫决策过程。利用在线学习工具，我们设计了一种原对偶在线优化算法。我们使用从真实数据随机生成的合成设置，涵盖了从平稳到非平稳的各种配置，对我们的方法进行了实证评估，并在约束违反和遗憾方面，与单独优化每个状态的知名基线方法进行了性能比较。