In the evolving landscape of digital commerce, adaptive dynamic pricing strategies are essential for gaining a competitive edge. This paper introduces novel {\em doubly nonparametric random utility models} that eschew traditional parametric assumptions used in estimating consumer demand's mean utility function and noise distribution. Existing nonparametric methods like multi-scale {\em Distributional Nearest Neighbors (DNN and TDNN)}, initially designed for offline regression, face challenges in dynamic online pricing due to design limitations, such as the indirect observability of utility-related variables and the absence of uniform convergence guarantees. We address these challenges with innovative population equations that facilitate nonparametric estimation within decision-making frameworks and establish new analytical results on the uniform convergence rates of DNN and TDNN, enhancing their applicability in dynamic environments. Our theoretical analysis confirms that the statistical learning rates for the mean utility function and noise distribution are minimax optimal. We also derive a regret bound that illustrates the critical interaction between model dimensionality and noise distribution smoothness, deepening our understanding of dynamic pricing under varied market conditions. These contributions offer substantial theoretical insights and practical tools for implementing effective, data-driven pricing strategies, advancing the theoretical framework of pricing models and providing robust methodologies for navigating the complexities of modern markets.

翻译：在数字商务不断演变的格局中，自适应动态定价策略对于获得竞争优势至关重要。本文引入了新颖的“双非参数随机效用模型”，该模型摒弃了传统用于估计消费者需求均值效用函数和噪声分布的参数假设。现有的非参数方法，如多尺度“分布最近邻（DNN和TDNN）”，最初是为离线回归设计的，但由于设计限制，在动态在线定价中面临挑战，例如效用相关变量的间接可观测性以及缺乏一致收敛性保证。我们通过创新的总体方程解决了这些挑战，该方程促进了决策框架内的非参数估计，并建立了关于DNN和TDNN一致收敛速率的新分析结果，增强了它们在动态环境中的适用性。我们的理论分析证实，均值效用函数和噪声分布的统计学习速率是极小化最优的。我们还推导了一个遗憾界，阐明了模型维度与噪声分布平滑性之间的关键相互作用，从而加深了对不同市场条件下动态定价的理解。这些贡献为实施有效的、数据驱动的定价策略提供了重要的理论见解和实用工具，推进了定价模型的理论框架，并为应对现代市场的复杂性提供了稳健的方法论。