Data Privacy in Pricing: Estimation Bias and Implications

Abstract

We study two privacy protection mechanisms motivated by emerging privacy regulations, limited retention and self-protection, in the context of data-driven (personalized) pricing. Limited retention refers to the removal of private data from a firm's database, and self-protection refers to a fraction of privacy-aware customers hiding their private information. Privacy protection affects the estimation of the demand model and, thus, the offered price. Assuming a linear demand curve, we find that, while the firm always earns lower revenues under privacy protection, which customer groups benefit from the protection depends on the product/service type. For inferior goods (e.g., those whose demand is negatively correlated with income as a focal private feature), offered prices would decrease for all customers due to limited retention, and counter-intuitively, under self-protection, privacy-protecting customers would see a price increase while privacy-unconscious customers would see a price decrease. The opposite results hold for normal goods (e.g., those whose demand is positively correlated with income). On the other hand, the magnitude of the resulting price change is greater for industries with stronger historical price personalization. We validate our theoretical findings with a real dataset of online auto loans which consists mostly of "inferior" loans. Remarkably, we indeed observe in extensive numerical experiments for self-protection that protective customers face consistent price increases, regardless of what features such customers protect. We extend the framework to nonlinear demand functions and a duopoly. In the duopoly, the situation can be that both firms earn higher revenues, whereas customers pay more under privacy protection, in contrast to the monopolistic setting.

Keywords: Privacy, Personalized Pricing, Model Estimation, Revenue Management