Pricing decisions of companies require an understanding of the causal effect of a price change on the demand. When real-life pricing experiments are infeasible, data-driven decision-making must be based on alternative data sources such as purchase history (sales data) and conjoint studies where a group of customers is asked to make imaginary purchases in an artificial setup. We present an approach for price optimization that combines population statistics, purchase history and conjoint data in a systematic way. We build on the recent advances in causal inference to identify and quantify the effect of price on the purchase probability at the customer level. The identification task is a transportability problem whose solution requires a parametric assumption on the differences between the conjoint study and real purchases. The causal effect is estimated using Bayesian methods that take into account the uncertainty of the data sources. The pricing decision is made by comparing the estimated posterior distributions of gross profit for different prices. The approach is demonstrated with simulated data resembling the features of real-world data.

翻译：企业的定价决策需要理解价格变化对需求的因果效应。当现实中的定价实验不可行时，数据驱动的决策必须基于替代数据源，例如购买历史（销售数据）和联合分析研究（在人工设定下邀请一组客户进行虚拟购买）。我们提出了一种系统性地结合总体统计数据、购买历史和联合数据进行价格优化的方法。我们基于因果推断领域的最新进展，在客户层面识别并量化价格对购买概率的影响。识别任务是一个可迁移性问题，其解决方案需要对联合研究与实际购买之间的差异进行参数化假设。因果效应采用贝叶斯方法进行估计，该方法考虑了数据源的不确定性。定价决策通过比较不同价格下毛利的事后分布来做出。该方法通过模拟具有真实世界数据特征的仿真数据进行了验证。