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Asymptotically Tight Bounds on the Optimal Pricing Strategy with Patient Customers

Author

Listed:
  • Shuaijie Qian

    (Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong)

  • Xizhi Su

    (Department of Mathematics, National University of Singapore, Singapore 119076)

  • Chao Zhou

    (Department of Mathematics, National University of Singapore, Singapore 119076; and Risk Management Institute, National University of Singapore, Singapore 119076)

Abstract

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.

Suggested Citation

  • Shuaijie Qian & Xizhi Su & Chao Zhou, 2025. "Asymptotically Tight Bounds on the Optimal Pricing Strategy with Patient Customers," Operations Research, INFORMS, vol. 73(2), pages 664-671, March.
    • Handle: RePEc:inm:oropre:v:73:y:2025:i:2:p:664-671
    DOI: 10.1287/opre.2021.0459
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