IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v229y2013i1p223-229.html
   My bibliography  Save this article

A continuous-time dynamic pricing model knowing the competitor’s pricing strategy

Author

Listed:
  • Sato, Kimitoshi
  • Sawaki, Katsushige

Abstract

In this paper we consider a dynamic pricing model for a firm knowing that a competitor adopts a static pricing strategy. We establish a continuous time model to analyze the effect of dynamic pricing on the improvement in expected revenue in the duopoly. We assume that customers arrive to purchase tickets in accordance with a geometric Brownian motion. We derive an explicit closed-form expression for an optimal pricing policy to maximize the expected revenue. It is shown that when the competitor adopts a static pricing policy, dynamic pricing is not always effective in terms of maximizing expected revenue compared to a fixed pricing strategy. Moreover, we show that the size of the reduction in the expected revenue depends on the competitor’s pricing strategy. Numerical results are presented to illustrate the dynamic pricing policy.

Suggested Citation

  • Sato, Kimitoshi & Sawaki, Katsushige, 2013. "A continuous-time dynamic pricing model knowing the competitor’s pricing strategy," European Journal of Operational Research, Elsevier, vol. 229(1), pages 223-229.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:1:p:223-229
    DOI: 10.1016/j.ejor.2013.02.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713001550
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.02.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marc Chesney & Luca Taschini, 2012. "The Endogenous Price Dynamics of Emission Allowances and an Application to CO 2 Option Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(5), pages 447-475, November.
    2. Guillermo Gallego & Garrett van Ryzin, 1997. "A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management," Operations Research, INFORMS, vol. 45(1), pages 24-41, February.
    3. Koenig, Matthias & Meissner, Joern, 2010. "List pricing versus dynamic pricing: Impact on the revenue risk," European Journal of Operational Research, Elsevier, vol. 204(3), pages 505-512, August.
    4. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    5. Xiaowei Xu & Wallace J. Hopp, 2006. "A Monopolistic and Oligopolistic Stochastic Flow Revenue Management Model," Operations Research, INFORMS, vol. 54(6), pages 1098-1109, December.
    6. Marcus, Benjamin & Anderson, Chris K., 2008. "Revenue management for low-cost providers," European Journal of Operational Research, Elsevier, vol. 188(1), pages 258-272, July.
    7. C S M Currie & R C H Cheng & H K Smith, 2008. "Dynamic pricing of airline tickets with competition," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(8), pages 1026-1037, August.
    8. Lin, Kyle Y. & Sibdari, Soheil Y., 2009. "Dynamic price competition with discrete customer choices," European Journal of Operational Research, Elsevier, vol. 197(3), pages 969-980, September.
    9. Yuri Levin & Jeff McGill & Mikhail Nediak, 2009. "Dynamic Pricing in the Presence of Strategic Consumers and Oligopolistic Competition," Management Science, INFORMS, vol. 55(1), pages 32-46, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yafei Zu & Fengyi Li & Yinfei Xu & Hui Zhang, 2024. "Low-carbon strategies in the alliance between manufacturer and weak customer considering different contracts," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 26(7), pages 17941-17965, July.
    2. Sato, Kimitoshi, 2019. "Price Trends and Dynamic Pricing in Perishable Product Market Consisting of Superior and Inferior Firms," European Journal of Operational Research, Elsevier, vol. 274(1), pages 214-226.
    3. Li, Mengmeng & Mizuno, Shinji, 2022. "Comparison of dynamic and static pricing strategies in a dual-channel supply chain with inventory control," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 165(C).
    4. Gandomi, Amir & Zolfaghari, Saeed, 2018. "To tier or not to tier: An analysis of multitier loyalty programs׳ optimality conditions," Omega, Elsevier, vol. 74(C), pages 20-36.
    5. Sun, Shuxiao & Zheng, Xiaona & Sun, Luping, 2020. "Multi-period pricing in the presence of competition and social influence," International Journal of Production Economics, Elsevier, vol. 227(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sato, Kimitoshi, 2019. "Price Trends and Dynamic Pricing in Perishable Product Market Consisting of Superior and Inferior Firms," European Journal of Operational Research, Elsevier, vol. 274(1), pages 214-226.
    2. Torsten J. Gerpott & Jan Berends, 2022. "Competitive pricing on online markets: a literature review," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(6), pages 596-622, December.
    3. Guillermo Gallego & Ming Hu, 2014. "Dynamic Pricing of Perishable Assets Under Competition," Management Science, INFORMS, vol. 60(5), pages 1241-1259, May.
    4. Ayelet Israeli & Fiona Scott-Morton & Jorge Silva-Risso & Florian Zettelmeyer, 2022. "How Market Power Affects Dynamic Pricing: Evidence from Inventory Fluctuations at Car Dealerships," Management Science, INFORMS, vol. 68(2), pages 895-916, February.
    5. Jian Yang & Yusen Xia & Xiangtong Qi & Yifeng Liu, 2014. "A nonatomic‐game model for timing clearance sales under competition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 365-385, August.
    6. Benny Mantin & Daniel Granot & Frieda Granot, 2011. "Dynamic pricing under first order Markovian competition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 608-617, September.
    7. Dasci, A. & Karakul, M., 2009. "Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly," European Journal of Operational Research, Elsevier, vol. 197(3), pages 945-968, September.
    8. Aniruddha Dutta, 2019. "Capacity Allocation of Game Tickets Using Dynamic Pricing," Data, MDPI, vol. 4(4), pages 1-12, October.
    9. Lingxiu Dong & Panos Kouvelis & Zhongjun Tian, 2009. "Dynamic Pricing and Inventory Control of Substitute Products," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 317-339, December.
    10. Sibdari, Soheil & Pyke, David F., 2010. "A competitive dynamic pricing model when demand is interdependent over time," European Journal of Operational Research, Elsevier, vol. 207(1), pages 330-338, November.
    11. Gu, Wei & Luo, Jing & Yu, Xiaoru & Zhang, Wenqing & Li, Baixun, 2023. "Dynamic decisions between sellers and consumers in online second-hand trading platforms: Evidence from C2C transactions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    12. Gisches, Eyran J. & Qi, Hang & Becker, William J. & Rapoport, Amnon, 2021. "Strategic retailers and myopic consumers: Competitive pricing of perishable goods," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 92(C).
    13. Ningyuan Chen & Guillermo Gallego, 2019. "Welfare Analysis of Dynamic Pricing," Management Science, INFORMS, vol. 65(1), pages 139-151, January.
    14. Kuo, Chia-Wei & Huang, Kwei-Long, 2012. "Dynamic pricing of limited inventories for multi-generation products," European Journal of Operational Research, Elsevier, vol. 217(2), pages 394-403.
    15. Andrew Sweeting, 2012. "Dynamic Pricing Behavior in Perishable Goods Markets: Evidence from Secondary Markets for Major League Baseball Tickets," Journal of Political Economy, University of Chicago Press, vol. 120(6), pages 1133-1172.
    16. Qi Feng & Yuanchen Li & J. George Shanthikumar, 2020. "Competitive Revenue Management with Sequential Bargaining," Production and Operations Management, Production and Operations Management Society, vol. 29(5), pages 1307-1324, May.
    17. Ioannis Stamatopoulos & Christos Tzamos, 2019. "Design and Dynamic Pricing of Vertically Differentiated Inventories," Management Science, INFORMS, vol. 65(9), pages 4222-4241, September.
    18. Zhang Wensi & Li Jinlin & Ran Lun, 2014. "Price Increasing Timing of Competitive Perishable Products," Journal of Systems Science and Information, De Gruyter, vol. 2(1), pages 29-37, February.
    19. Ming Chen & Zhi-Long Chen, 2018. "Robust Dynamic Pricing with Two Substitutable Products," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 249-268, May.
    20. Qian Liu & Dan Zhang, 2013. "Dynamic Pricing Competition with Strategic Customers Under Vertical Product Differentiation," Management Science, INFORMS, vol. 59(1), pages 84-101, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:229:y:2013:i:1:p:223-229. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.