Is Your Price Personalized? Alleviating Customer Concerns with Inventory Availability Information

We study a firm setting prices for a product with limited inventories sold over two periods to heterogeneous customers. The firm is uncertain about customer valuations and learns from their purchasing behavior. This information can be used for future personalized pricing (P-Pricing). The firm can be of two types; a P-type firm may implement P-Pricing, whereas a U-type firm must set uniform prices for all customers. Customers are uncertain about the firm type and inventory. Upon observing the first-period price, they update their beliefs about P-Pricing implementation and may forgo a purchase if they believe revealing their valuations would significantly reduce their future utility due to P-Pricing. We investigate whether and when price can serve as an instrument to signal the implementation of P-Pricing to customers. We show that the price alone is insufficient to perfectly resolve uncertainty about P-Pricing. This uncertainty induces behavior that harms both the firm and customers. We identify conditions under which a binary inventory signal complements the price and further resolves this uncertainty. Additionally, such a signal can simultaneously increase the firm’s revenue and benefit customers. We establish the robustness of our insights through a series of extensions.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2023.0360.