Pricing based on individual customer characteristics is widely used to maximize sellers' revenues. This work studies offline personalized pricing under endogeneity using an instrumental variable approach. Standard instrumental variable methods in causal inference/econometrics either focus on a discrete treatment space or require the exclusion restriction of instruments from having a direct effect on the outcome, which limits their applicability in personalized pricing. In this paper, we propose a new policy learning method for Personalized pRicing using Invalid iNsTrumental variables (PRINT) for continuous treatment that allow direct effects on the outcome. Specifically, relying on the structural models of revenue and price, we establish the identifiability condition of an optimal pricing strategy under endogeneity with the help of invalid instrumental variables. Based on this new identification, which leads to solving conditional moment restrictions with generalized residual functions, we construct an adversarial min-max estimator and learn an optimal pricing strategy. Furthermore, we establish an asymptotic regret bound to find an optimal pricing strategy. Finally, we demonstrate the effectiveness of the proposed method via extensive simulation studies as well as a real data application from an US online auto loan company.
翻译:基于个别客户特点的定价被广泛用于最大限度地增加卖方的收入。本项工作采用一种工具变量方法,在内分质法下对内分泌的个人化定价进行离线研究。因果推断/经济计量的标准工具变量方法要么侧重于离散处理空间,要么要求排除工具对结果产生直接影响,从而限制其在个人化定价中的适用性。在本文件中,我们提出一种新的政策学习方法,用于使用无效的iNSTrument变量(PRINT)进行个性化学习,以持续处理,从而能够对结果产生直接影响。具体地说,我们依靠收入和价格的结构模型,在无效的工具变量的帮助下,在内分泌下确定最佳定价战略的可识别性条件。基于这一新的识别方法,通过普遍残留功能解决有条件的时段限制,我们建立了一个对抗性的微量估计器,并学习最佳定价战略。此外,我们建立了一种无谓的遗憾,以便找到最佳定价战略。最后,我们通过广泛的模拟研究,以及美国在线自动贷款公司的实际数据应用,展示了拟议方法的有效性。</s>