We study competitive dynamic pricing among multiple sellers, motivated by the rise of large-scale experimentation and algorithmic pricing in retail and online marketplaces. Sellers repeatedly set prices using simple learning rules and observe their own realized demand, while possibly observing only a subset of rivals' prices, even though demand depends on all sellers' prices and is subject to random shocks. Each seller runs local price experiments, such as switchback-style designs, and updates a focal price using a linear demand estimate fitted to its own demand data and the competitor prices it observes. Under certain conditions on demand, the resulting dynamics converge to a Conjectural Variations (CV) equilibrium, a classic static equilibrium notion in which each seller best responds under a conjecture that rivals' prices co-move systematically to changes in its own price. Unlike standard CV models that treat conjectures as behavioral primitives, we show that these conjectures arise endogenously from the interaction between the feedback structure and the correlation structure of experimentation. When a seller does not observe some rivals' prices, correlated experimentation induces an omitted-variable bias in demand estimation. We show that this bias determines the conjectures that govern the long-run equilibrium. Notably, when this learning bias vanishes, for example under full price feedback or independent experimentation of unobserved rivals, the learning dynamics converge to the standard Nash equilibrium. We provide simple sufficient conditions on demand for convergence in standard models and establish a finite-sample guarantee, showing that the mean squared price error decays at a rate of $\widetilde O (T^{-1/2})$.

翻译：我们研究多个卖家之间的竞争性动态定价问题，这一研究受到零售与在线市场中大规模实验与算法定价兴起的启发。卖家通过简单学习规则重复设定价格，并观察自身实现的真实需求，但可能仅观察到部分竞争对手的价格——尽管需求取决于所有卖家的价格并受随机冲击影响。每位卖家执行局部价格实验（如切换式设计），并基于自身需求数据及所观测到的竞争对手价格拟合线性需求估计，从而更新焦点价格。在特定需求条件下，由此产生的动态过程收敛至揣测变分均衡——这是一种经典静态均衡概念：每位卖家在“竞争对手价格会随自身价格系统性协同变动”的揣测下做出最优反应。不同于将揣测视为行为基元的传统CV模型，我们证明这些揣测内生于反馈结构与实验相关性结构的交互作用。当卖家未能观测到某些竞争对手的价格时，关联实验会在需求估计中引发遗漏变量偏差。我们证明这种偏差决定了主导长期均衡的揣测。值得注意的是，当这种学习偏差消失时（例如在完全价格反馈或未观测竞争对手独立实验的情形下），学习动态收敛至标准纳什均衡。我们为标准模型中的收敛性给出了简单的需求充分条件，并建立了有限样本保证，表明价格均方误差以$\widetilde O (T^{-1/2})$速率衰减。