Personalized Dynamic Pricing of Limited Inventories

Prior work has investigated time and inventory-level dependent pricing of limited inventories with finite selling horizons. We consider a third dimension in addition to time and inventory level that the firms can use in setting their prices: the information that the firm has at the individual customer level. An arriving customer provides a signal to the firm, which is an imperfect indicator of the customer’s willingness-to-pay, and the firm makes a personalized price offer depending on the signal, inventory level, and time. We consider two different models: full personalization and partial personalization. In full personalization model, the firm charges any price it wishes given the customer signal, while in the partial personalization model, the firm can charge one of two prices. We find that a mere correlation between the signals and customers’ willingness-to-pay is not sufficient to ensure intuitive relationships between the signal and the optimal prices. We determine a stronger condition, which leads to several structural properties including the monotonicity of the optimal price with respect to the signal in the full personalization model. For the partial personalization model, we show that the optimal pricing policy is of threshold-type and that the threshold is monotonic in the inventory level and time. Through a numerical study, we investigate the interactions between personalized pricing and dynamic pricing. In an extension model where signals from some of the customers are not available, we find that it might in fact be better for the firm if customers with high willingness-to-pay do not provide their signals, since it helps the firm better price-discriminate.