Protecting Consumers Against Personalized Pricing: A Stopping Time Approach

The widespread availability of behavioral data has led to the development of data-driven personalized pricing algorithms: sellers attempt to maximize their revenue by estimating the consumer's willingness-to-pay and pricing accordingly. Our objective is to develop algorithms that protect consumer interests against personalized pricing schemes. In this paper, we consider a consumer who learns more and more about a potential purchase across time, while simultaneously revealing more and more information about herself to a potential seller. We formalize a strategic consumer's purchasing decision when interacting with a seller who uses personalized pricing algorithms, and contextualize this problem among the existing literature in optimal stopping time theory and computational finance. We provide an algorithm that consumers can use to protect their own interests against personalized pricing algorithms. This algorithmic stopping method uses sample paths to train estimates of the optimal stopping time. To the best of our knowledge, this is one of the first works that provides computational methods for the consumer to maximize her utility when decision making under surveillance. We demonstrate the efficacy of the algorithmic stopping method using a numerical simulation, where the seller uses a Kalman filter to approximate the consumer's valuation and sets prices based on myopic expected revenue maximization. Compared to a myopic purchasing strategy, we demonstrate increased payoffs for the consumer in expectation.