Pricing Experimental Design: Causal Effect, Expected Revenue and Tail Risk

Abstract

When launching a new product, historical sales data is often not available, leaving price as a crucial experimental instrument for sellers to gauge market response. When designing pricing experiments, there are three fundamental objectives: estimating the causal effect of price (i.e., price elasticity), maximizing the expected revenue through the experiment, and controlling the tail risk suffering from a very huge loss. In this paper, we reveal the relationship among such three objectives. Under a linear structural model, we investigate the trade-offs between causal inference and expected revenue maximization, as well as between expected revenue maximization and tail risk control. Furthermore, we propose an optimal pricing experimental design, which can flexibly adapt to different desired levels of trade-offs. We also explore the relationship between causal inference and tail risk control. Finally, we extend our results and the design to a misspecified setting, where the structural model is not necessarily linear but the seller still runs our design for linear structural models. The results demonstrate the robustness of our design and the wide existence of the relationships among the three objectives.

Keywords: Adaptive Experimental Design, Treatment Effect, Revenue Management, Online Learning, Risk Control, Dynamic Pricing