Asymptotically Tight Bounds on the Optimal Pricing Strategy with Patient Customers

This work considers a monopolist seller facing both patient and impatient customers. Given the current price, the impatient customers will either purchase or leave immediately, depending on the relative magnitude between this price and their valuation of the product. In comparison, the patient customers will wait for some periods to see if the price will drop to their valuation, and if that occurs, they will purchase immediately. The monopolist designs the pricing strategy to maximize the long-run average revenue from them. We give tight bounds on both the optimal strategy’s cycle period and the optimal revenue when the patient customers possess a high patience level. This result answers the open question of the optimal cycle period raised by extant work. Later we also extend our theoretical result to the general case with multiple patience levels.

Funding: C. Zhou is supported in part by NSFC [Grant 11871364] and IoTeX Foundation Industry [Grant A-8001180-00-00].

Supplemental Material: The computer code and data that support the findings of this study are available within this article’s supplemental material at https://doi.org/10.1287/opre.2021.0459.