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Technical Note—Dynamic Pricing with Gain-Seeking Reference Price Effects

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  • Zhenyu Hu

    (Department of Decision Sciences, NUS Business School, National University of Singapore, Singapore 119245)

  • Xin Chen

    (Department of Industrial Enterprise and Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801)

  • Peng Hu

    (School of Management, Huazhong University of Science and Technology, 430074 Wuhan, China)

Abstract

We study a dynamic pricing problem of a firm facing reference price effects at an aggregate demand level, where demand is more sensitive to gains than losses. We find that even the myopic pricing strategy belongs to one type of discontinuous maps, which can exhibit complex dynamics over time. Our numerical examples show that, in general, the optimal pricing strategies may not admit any simple characterizations and the resulting reference price/price dynamics can be very complicated. We then show for a special case that a cyclic skimming pricing strategy is optimal, and we provide conditions to guarantee the optimality of high-low pricing strategies.

Suggested Citation

  • Zhenyu Hu & Xin Chen & Peng Hu, 2016. "Technical Note—Dynamic Pricing with Gain-Seeking Reference Price Effects," Operations Research, INFORMS, vol. 64(1), pages 150-157, February.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:1:p:150-157
    DOI: 10.1287/opre.2015.1445
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    References listed on IDEAS

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    1. Mayhew, Glenn E & Winer, Russell S, 1992. "An Empirical Analysis of Internal and External Reference Prices Using Scanner Data," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 19(1), pages 62-70, June.
    2. John Conlisk & Eitan Gerstner & Joel Sobel, 1984. "Cyclic Pricing by a Durable Goods Monopolist," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 99(3), pages 489-505.
    3. Briesch, Richard A, et al, 1997. "A Comparative Analysis of Reference Price Models," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 24(2), pages 202-214, September.
    4. Eric A. Greenleaf, 1995. "The Impact of Reference Price Effects on the Profitability of Price Promotions," Marketing Science, INFORMS, vol. 14(1), pages 82-104.
    5. Krishnamurthi, Lakshman & Mazumdar, Tridib & Raj, S P, 1992. "Asymmetric Response to Price in Consumer Brand Choice and Purchase Quantity Decisions," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 19(3), pages 387-400, December.
    6. Omar Besbes & Ilan Lobel, 2015. "Intertemporal Price Discrimination: Structure and Computation of Optimal Policies," Management Science, INFORMS, vol. 61(1), pages 92-110, January.
    7. Javad Nasiry & Ioana Popescu, 2011. "Dynamic Pricing with Loss-Averse Consumers and Peak-End Anchoring," Operations Research, INFORMS, vol. 59(6), pages 1361-1368, December.
    8. Yan Liu & William L. Cooper, 2015. "Optimal Dynamic Pricing with Patient Customers," Operations Research, INFORMS, vol. 63(6), pages 1307-1319, December.
    9. Gadi Fibich & Arieh Gavious & Oded Lowengart, 2003. "Explicit Solutions of Optimization Models and Differential Games with Nonsmooth (Asymmetric) Reference-Price Effects," Operations Research, INFORMS, vol. 51(5), pages 721-734, October.
    10. A. RamaN & F.M. Bass, 2002. "A gereral test of reference price theory in the presence of threshold effects," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 205-226.
    11. Ioana Popescu & Yaozhong Wu, 2007. "Dynamic Pricing Strategies with Reference Effects," Operations Research, INFORMS, vol. 55(3), pages 413-429, June.
    12. Praveen K. Kopalle & Ambar G. Rao & João L. Assunção, 1996. "Asymmetric Reference Price Effects and Dynamic Pricing Policies," Marketing Science, INFORMS, vol. 15(1), pages 60-85.
    13. Kopalle, Praveen K. & Kannan, P.K. & Boldt, Lin Bao & Arora, Neeraj, 2012. "The impact of household level heterogeneity in reference price effects on optimal retailer pricing policies," Journal of Retailing, Elsevier, vol. 88(1), pages 102-114.
    14. Hyun-soo Ahn & Mehmet Gümüş & Philip Kaminsky, 2007. "Pricing and Manufacturing Decisions When Demand Is a Function of Prices in Multiple Periods," Operations Research, INFORMS, vol. 55(6), pages 1039-1057, December.
    15. Robert Slonim & Ellen Garbarino, 2009. "Similarities and differences between stockpiling and reference effects," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 30(6), pages 351-371.
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    Cited by:

    1. Ilan Lobel, 2020. "Technical Note—Dynamic Pricing with Heterogeneous Patience Levels," Operations Research, INFORMS, vol. 68(4), pages 1038-1046, July.
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    3. Victor F. Araman & Bassam Fayad, 2021. "Intertemporal Price Discrimination with Time-Varying Valuations," Operations Research, INFORMS, vol. 69(1), pages 245-265, January.
    4. Kirshner, Samuel N. & Shao, Lusheng, 2018. "Internal and external reference effects in a two-tier supply chain," European Journal of Operational Research, Elsevier, vol. 267(3), pages 944-957.
    5. Cao, Ping & Zhao, Nenggui & Wu, Jie, 2019. "Dynamic pricing with Bayesian demand learning and reference price effect," European Journal of Operational Research, Elsevier, vol. 279(2), pages 540-556.
    6. Salgado Alfredo, 2022. "Regulation through Reference Prices," Working Papers 2022-05, Banco de México.
    7. Chenavaz, Régis & Paraschiv, Corina, 2018. "Dynamic pricing for inventories with reference price effects," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-16.
    8. Yan, Xiaoming & Chao, Xiuli & Lu, Ye, 2024. "Optimal control policies for dynamic inventory systems with service level dependent demand," European Journal of Operational Research, Elsevier, vol. 314(3), pages 935-949.
    9. Ma, Deqing & Li, Kaifu & Hu, Jinsong & Wang, Xue, 2024. "How to leverage blockchain to react to consumer reference effects and develop a distribution strategy in online retailing?," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 187(C).
    10. Zhang, Jie & Chiang, Wei-yu Kevin, 2020. "Durable goods pricing with reference price effects," Omega, Elsevier, vol. 91(C).
    11. Yiwei Chen & Vivek F. Farias & Nikolaos Trichakis, 2019. "On the Efficacy of Static Prices for Revenue Management in the Face of Strategic Customers," Management Science, INFORMS, vol. 65(12), pages 5535-5555, December.
    12. Georgia Perakis & Melvyn Sim & Qinshen Tang & Peng Xiong, 2023. "Robust Pricing and Production with Information Partitioning and Adaptation," Management Science, INFORMS, vol. 69(3), pages 1398-1419, March.
    13. Xin Chen & Peng Hu & Stephen Shum & Yuhan Zhang, 2016. "Dynamic Stochastic Inventory Management with Reference Price Effects," Operations Research, INFORMS, vol. 64(6), pages 1529-1536, December.
    14. Guang Yang & Ying Wang & Mulin Liu, 2023. "Optimal Policy for Probabilistic Selling with Three-Way Revenue Sharing Contract under the Perspective of Sustainable Supply Chain," Sustainability, MDPI, vol. 15(4), pages 1-22, February.
    15. Junhai Ma & Zhanbing Guo, 2017. "Implications for Firms with Limited Information to Take Advantage of Reference Price Effect in Competitive Settings," Complexity, Hindawi, vol. 2017, pages 1-16, June.
    16. Turunç Ömer & Karayalçın Cem, 2024. "Bridging Brand Parity with Insights Regarding Consumer Behavior," Economics - The Open-Access, Open-Assessment Journal, De Gruyter, vol. 18(1), pages 1-10, January.
    17. Bertrand Crettez & Naila Hayek & Georges Zaccour, 2020. "Existence and characterization of optimal dynamic pricing strategies with reference-price effects," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 441-459, June.
    18. Anton, Ramona & Chenavaz, Régis Y. & Paraschiv, Corina, 2023. "Dynamic pricing, reference price, and price-quality relationship," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    19. Hsieh, Tsu-Pang & Dye, Chung-Yuan, 2017. "Optimal dynamic pricing for deteriorating items with reference price effects when inventories stimulate demand," European Journal of Operational Research, Elsevier, vol. 262(1), pages 136-150.

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