卖家在动态定价中通过估计需求函数，实现价格收敛与低后悔率。
Revenue Maximization Under Sequential Price Competition Via The Estimation Of s-Concave Demand Functions
- 用半参数最小二乘法估计非线性需求函数，指导动态定价。
- 价格以 $O(T^{-1/7})$ 速度收敛到纳什均衡，单个卖家后悔率为 $O(T^{5/7})$。
- 适用于竞争环境下需学习策略的商家，尤其适合非参数学习研究者。
我们研究多个卖家在 $T$ 期销售周期内的价格竞争。每期，卖家同时公布价格并观察自身需求（不公开）。每个卖家的需求依赖于所有卖家价格的私有、未知且非线性关系。本文提出一种动态定价策略，采用半参数最小二乘估计，证明当卖家采用该策略时，其价格以 $O(T^{-1/7})$ 的速率收敛至完全信息下的纳什均衡价格；每个卖家相对于动态基准策略的后悔率为 $O(T^{5/7})$。理论贡献在于通过 $s$-凹性概念证明了形状约束需求函数下的均衡存在性，并建立了所提策略的后悔界。技术上，还给出了形状约束下最小二乘估计的新浓度结果。研究为动态竞争感知定价提供了深刻洞见，推动了非参数学习在战略决策中的应用。
原文摘要 · Abstract (English)
We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices (which are made public) and subsequently observe their respective demand (not made public). The demand function of each seller depends on all sellers' prices through a private, unknown, and nonlinear relationship. We propose a dynamic pricing policy that uses semi-parametric least-squares estimation and show that when the sellers employ our policy, their prices converge at a rate of $O(T^{-1/7})$ to the Nash equilibrium prices that sellers would reach if they were fully informed. Each seller incurs a regret of $O(T^{5/7})$ relative to a dynamic benchmark policy. A theoretical contribution of our work is proving the existence of equilibrium under shape-constrained demand functions via the concept of $s$-concavity and establishing regret bounds of our proposed policy. Technically, we also establish new concentration results for the least squares estimator under shape constraints. Our findings offer significant insights into dynamic competition-aware pricing and contribute to the broader study of non-parametric learning in strategic decision-making.
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