IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v35y1988i3p397-409.html
   My bibliography  Save this article

Game theoretic analysis of the substitutable product inventory problem with random demands

Author

Listed:
  • Mahmut Parlar

Abstract

This article uses game theoretic concepts to analyze the inventory problem with two substitutable products having random demands. It is assumed that the two decision makers (players) who make ordering decisions know the substitution rates and the demand densities for both products. Since each player's decision affects the other's single‐period expected profit, game theory is used to find the order quantities when the players use a Nash strategy (i.e., they act rationally). We prove the existence and uniqueness of the Nash solution. It is also shown that when one of the players acts irrationally for the sole purpose of inflicting maximum damage on the other, the maximin strategy for the latter reduces to using the solution for the classical single‐period inventory problem. We also discuss the cooperative game and prove that the players always gain if they cooperate and maximize a joint objective function.

Suggested Citation

  • Mahmut Parlar, 1988. "Game theoretic analysis of the substitutable product inventory problem with random demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(3), pages 397-409, June.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:3:p:397-409
    DOI: 10.1002/1520-6750(198806)35:33.0.CO;2-Z
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198806)35:33.0.CO;2-Z
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198806)35:33.0.CO;2-Z?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
    ---><---

    References listed on IDEAS

    as
    1. Kenneth R. Deal, 1979. "Optimizing Advertising Expenditures in a Dynamic Duopoly," Operations Research, INFORMS, vol. 27(4), pages 682-692, August.
    Full references (including those not matched with items on IDEAS)

    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. Fruchter, Gila E. & Kalish, Shlomo, 1998. "Dynamic promotional budgeting and media allocation," European Journal of Operational Research, Elsevier, vol. 111(1), pages 15-27, November.
    2. Mesak, Hani I. & Calloway, James A., 1995. "A pulsing model of advertising competition: A game theoretic approach, part A -- Theoretical foundation," European Journal of Operational Research, Elsevier, vol. 86(2), pages 231-248, October.
    3. Krishnamoorthy, Anand & Prasad, Ashutosh & Sethi, Suresh P., 2010. "Optimal pricing and advertising in a durable-good duopoly," European Journal of Operational Research, Elsevier, vol. 200(2), pages 486-497, January.
    4. Anshuman Chutani & Suresh Sethi, 2012. "Cooperative Advertising in a Dynamic Retail Market Oligopoly," Dynamic Games and Applications, Springer, vol. 2(4), pages 347-375, December.
    5. Dengpan Liu & Subodha Kumar & Vijay S. Mookerjee, 2020. "Flexible and Committed Advertising Contracts in Electronic Retailing," Information Systems Research, INFORMS, vol. 31(2), pages 323-339, June.
    6. Richards, Timothy J., 2002. "Dynamic Strategic Interaction: A Synthesis Of Modeling Methods," Western Economics Forum, Western Agricultural Economics Association, vol. 1(1), pages 1-5.
    7. Parker, Philip M. & Sarvary, Miklos, 1997. "Formulating dynamic strategies using decision calculus," European Journal of Operational Research, Elsevier, vol. 98(3), pages 542-554, May.
    8. Hui Li & Qiaowei Shen & Yakov Bart, 2021. "Dynamic Resource Allocation on Multi-Category Two-Sided Platforms," Management Science, INFORMS, vol. 67(2), pages 984-1003, February.
    9. Erickson, Gary M., 1995. "Differential game models of advertising competition," European Journal of Operational Research, Elsevier, vol. 83(3), pages 431-438, June.
    10. Berger, Paul D. & Bechwati, Nada Nasr, 2001. "The allocation of promotion budget to maximize customer equity," Omega, Elsevier, vol. 29(1), pages 49-61, February.
    11. Katarina Valaskova & Marek Durica & Maria Kovacova & Elena Gregova & George Lazaroiu, 2019. "Oligopolistic Competition among Providers in the Telecommunication Industry: The Case of Slovakia," Administrative Sciences, MDPI, vol. 9(3), pages 1-15, June.
    12. G. Fruchter & G. M. Erickson & S. Kalish, 2001. "Feedback Competitive Advertising Strategies with a General Objective Function," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 601-613, June.
    13. Marshall Freimer & Dan Horsky, 2012. "Periodic Advertising Pulsing in a Competitive Market," Marketing Science, INFORMS, vol. 31(4), pages 637-648, July.
    14. Machowska Dominika, 2018. "Investigating the role of customer churn in the optimal allocation of offensive and defensive advertising: the case of the competitive growing market," Economics and Business Review, Sciendo, vol. 4(2), pages 3-23, June.
    15. Prasad A. Naik & Kalyan Raman & Russell S. Winer, 2005. "Planning Marketing-Mix Strategies in the Presence of Interaction Effects," Marketing Science, INFORMS, vol. 24(1), pages 25-34, June.
    16. Fruchter, Gila E. & Messinger, Paul R., 2003. "Optimal management of fringe entry over time," Journal of Economic Dynamics and Control, Elsevier, vol. 28(3), pages 445-466, December.
    17. Toker Doganoglu & Daniel Klapper, 2006. "Goodwill and dynamic advertising strategies," Quantitative Marketing and Economics (QME), Springer, vol. 4(1), pages 5-29, March.
    18. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    19. Nawel Amrouche & Guiomar Martín-Herrán & Georges Zaccour, 2008. "Feedback Stackelberg equilibrium strategies when the private label competes with the national brand," Annals of Operations Research, Springer, vol. 164(1), pages 79-95, November.
    20. Karray, Salma & Martín-Herrán, Guiomar, 2009. "A dynamic model for advertising and pricing competition between national and store brands," European Journal of Operational Research, Elsevier, vol. 193(2), pages 451-467, March.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:35:y:1988:i:3:p:397-409. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.