Learning effective pricing strategies is crucial in digital marketplaces, especially when buyers' valuations are unknown and must be inferred through interaction. We study the online contextual pricing problem, where a seller observes a stream of context-valuation pairs and dynamically sets prices. Moreover, departing from traditional online learning frameworks, we consider a strategic setting in which buyers may misreport valuations to influence future prices, a challenge known as strategic overfitting (Amin et al. 2013). We introduce a strategy-robust notion of regret for multi-buyer online environments, capturing worst-case strategic behavior in the spirit of the Price of Anarchy. Our first contribution is a polynomial-time approximation scheme (PTAS) for learning linear pricing policies in adversarial, adaptive environments, enabled by a novel online sketching technique. Building on this result, we propose our main construction: the Sparse Update Mechanism (SUM), a simple yet effective sequential mechanism that ensures robustness to all Nash equilibria among buyers. Moreover, our construction yields a black-box reduction from online expert algorithms to strategy-robust learners.

翻译：在数字市场中学习有效的定价策略至关重要，尤其是在买家估值未知且必须通过交互推断的情况下。我们研究了在线上下文定价问题，其中卖家观察一系列上下文-估值对并动态设定价格。此外，与传统在线学习框架不同，我们考虑了一个策略性环境，其中买家可能误报估值以影响未来价格，这一挑战被称为策略性过拟合（Amin等人，2013）。我们为多买家在线环境引入了一种策略鲁棒的遗憾概念，以无政府价格比的精神捕捉最坏情况下的策略行为。我们的第一个贡献是针对对抗性、自适应环境中学习线性定价策略的多项式时间近似方案（PTAS），该方案通过一种新颖的在线草图技术实现。基于此结果，我们提出了主要构建：稀疏更新机制（SUM），这是一种简单而有效的序贯机制，确保对买家间所有纳什均衡的鲁棒性。此外，我们的构建实现了从在线专家算法到策略鲁棒学习器的黑盒归约。