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On the Minimax Complexity of Pricing in a Changing Environment

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  • Omar Besbes

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Assaf Zeevi

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

We consider a pricing problem in an environment where the customers' willingness-to-pay (WtP) distribution may change at some point over the selling horizon. Customers arrive sequentially and make purchase decisions based on a quoted price and their private reservation price. The seller knows the WtP distribution pre- and postchange but does not know the time at which this change occurs. The performance of a pricing policy is measured in terms of regret: the loss in revenues relative to an oracle that knows the time of change prior to the start of the selling season. We derive lower bounds on the worst-case regret and develop pricing strategies that achieve the order of these bounds, thus establishing the complexity of the pricing problem. Our results shed light on the role of price experimentation and its necessity for optimal detection of changes in market response/WtP. Our formulation allows for essentially arbitrary consumer WtP distributions and purchase request patterns.

Suggested Citation

  • Omar Besbes & Assaf Zeevi, 2011. "On the Minimax Complexity of Pricing in a Changing Environment," Operations Research, INFORMS, vol. 59(1), pages 66-79, February.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:1:p:66-79
    DOI: 10.1287/opre.1100.0867
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    References listed on IDEAS

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    Cited by:

    1. Omar Besbes & Assaf Zeevi, 2012. "Blind Network Revenue Management," Operations Research, INFORMS, vol. 60(6), pages 1537-1550, December.
    2. Giovanni Gatti Pinheiro & Thomas Fiig & Michael D. Wittman & Michael Defoin-Platel & Riccardo D. Jadanza, 2022. "Demand change detection in airline revenue management," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(6), pages 581-595, December.
    3. Arnoud V. den Boer & N. Bora Keskin, 2020. "Discontinuous Demand Functions: Estimation and Pricing," Management Science, INFORMS, vol. 66(10), pages 4516-4534, October.
    4. Moshe Haviv & Ramandeep S. Randhawa, 2014. "Pricing in Queues Without Demand Information," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 401-411, July.
    5. Kasberger, Bernhard & Woodward, Kyle, 2021. "Bidding in Multi-Unit Auctions under Limited Information," MPRA Paper 111185, University Library of Munich, Germany.
    6. Arnoud V. den Boer & Bert Zwart, 2015. "Dynamic Pricing and Learning with Finite Inventories," Operations Research, INFORMS, vol. 63(4), pages 965-978, August.
    7. Benjamin R. Handel & Kanishka Misra, 2015. "Robust New Product Pricing," Marketing Science, INFORMS, vol. 34(6), pages 864-881, November.
    8. den Boer, Arnoud V., 2015. "Tracking the market: Dynamic pricing and learning in a changing environment," European Journal of Operational Research, Elsevier, vol. 247(3), pages 914-927.
    9. N. Bora Keskin & Assaf Zeevi, 2017. "Chasing Demand: Learning and Earning in a Changing Environment," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 277-307, May.
    10. N. Bora Keskin & Assaf Zeevi, 2014. "Dynamic Pricing with an Unknown Demand Model: Asymptotically Optimal Semi-Myopic Policies," Operations Research, INFORMS, vol. 62(5), pages 1142-1167, October.
    11. Omar Besbes & Denis Sauré, 2014. "Dynamic Pricing Strategies in the Presence of Demand Shifts," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 513-528, October.
    12. Kazemi, Mohammad Sadegh & Fotopoulos, Stergios B. & Wang, Xinchang, 2023. "Minimizing online retailers’ revenue loss under a time-varying willingness-to-pay distribution," International Journal of Production Economics, Elsevier, vol. 257(C).
    13. Omar Besbes & Yonatan Gur & Assaf Zeevi, 2015. "Non-Stationary Stochastic Optimization," Operations Research, INFORMS, vol. 63(5), pages 1227-1244, October.
    14. Arnoud V. den Boer & Bert Zwart, 2014. "Simultaneously Learning and Optimizing Using Controlled Variance Pricing," Management Science, INFORMS, vol. 60(3), pages 770-783, March.
    15. Yusen Xia & Jian Yang & Tingting Zhou, 2019. "Revenue management under randomly evolving economic conditions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 73-89, February.
    16. Wang Chi Cheung & Will Ma & David Simchi-Levi & Xinshang Wang, 2022. "Inventory Balancing with Online Learning," Management Science, INFORMS, vol. 68(3), pages 1776-1807, March.
    17. Negin Golrezaei & Hamid Nazerzadeh & Paat Rusmevichientong, 2014. "Real-Time Optimization of Personalized Assortments," Management Science, INFORMS, vol. 60(6), pages 1532-1551, June.
    18. Josef Broder & Paat Rusmevichientong, 2012. "Dynamic Pricing Under a General Parametric Choice Model," Operations Research, INFORMS, vol. 60(4), pages 965-980, August.
    19. Ying Zhong & L. Jeff Hong & Guangwu Liu, 2021. "Earning and Learning with Varying Cost," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2379-2394, August.
    20. H. Müge Yayla‐Küllü & Jennifer K. Ryan & Jayashankar M. Swaminathan, 2021. "Product Line Flexibility for Agile and Adaptable Operations," Production and Operations Management, Production and Operations Management Society, vol. 30(3), pages 725-737, March.
    21. Xuejun Zhao & Ruihao Zhu & William B. Haskell, 2022. "Learning to Price Supply Chain Contracts against a Learning Retailer," Papers 2211.04586, arXiv.org.
    22. N. Bora Keskin & Yuexing Li & Jing-Sheng Song, 2022. "Data-Driven Dynamic Pricing and Ordering with Perishable Inventory in a Changing Environment," Management Science, INFORMS, vol. 68(3), pages 1938-1958, March.
    23. Boxiao Chen, 2021. "Data‐Driven Inventory Control with Shifting Demand," Production and Operations Management, Production and Operations Management Society, vol. 30(5), pages 1365-1385, May.
    24. Arnoud V. den Boer, 2014. "Dynamic Pricing with Multiple Products and Partially Specified Demand Distribution," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 863-888, August.

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