IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v52y2006i5p804-811.html
   My bibliography  Save this article

A Note on Feedback Sequential Equilibria in a Lanchester Model with Empirical Application

Author

Listed:
  • Michèle Breton

    (CREF and GERAD, HEC Montréal, Montréal, Québec, Canada H3T 2A7)

  • Ramla Jarrar

    (Ohal Limited, WPP, 5-11 Lee Road, BlackHeath, London, United Kingdom SE3 9RQ)

  • Georges Zaccour

    (GERAD, HEC Montréal, Montréal, Québec, Canada H3T 2A7)

Abstract

We study in this paper dynamic equilibrium advertising strategies in a duopoly with asymmetric information structure and sequential play. The advertising model of Lanchester is used in a game where the relevant solution concept is feedback Stackelberg equilibrium, which is subgame perfect. An algorithm is devised for the computation of this equilibrium, and numerical results are reported and discussed. Using a data set from the cola market, we obtain the resulting advertising strategies and provide a comparison with closed-loop and open-loop Nash equilibria.

Suggested Citation

  • Michèle Breton & Ramla Jarrar & Georges Zaccour, 2006. "A Note on Feedback Sequential Equilibria in a Lanchester Model with Empirical Application," Management Science, INFORMS, vol. 52(5), pages 804-811, May.
    • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:5:p:804-811
    DOI: 10.1287/mnsc.1050.0475
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1050.0475
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1050.0475?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. Gary M. Erickson, 1992. "Empirical Analysis of Closed-Loop Duopoly Advertising Strategies," Management Science, INFORMS, vol. 38(12), pages 1732-1749, December.
    2. Pradeep K. Chintagunta & Naufel J. Vilcassim, 1992. "An Empirical Investigation of Advertising Strategies in a Dynamic Duopoly," Management Science, INFORMS, vol. 38(9), pages 1230-1244, September.
    3. Gila E. Fruchter & Shlomo Kalish, 1997. "Closed-Loop Advertising Strategies in a Duopoly," Management Science, INFORMS, vol. 43(1), pages 54-63, January.
    4. Ramla Jarrar & Guiomar Martín-Herrán & Georges Zaccour, 2004. "Markov Perfect Equilibrium Advertising Strategies of Lanchester Duopoly Model: A Technical Note," Management Science, INFORMS, vol. 50(7), pages 995-1000, July.
    5. Sorger, Gerhard, 1989. "Competitive dynamic advertising : A modification of the Case game," Journal of Economic Dynamics and Control, Elsevier, vol. 13(1), pages 55-80, 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. Mesak, Hani I. & Bari, Abdullahel & Blackstock, Rob, 2016. "On the robustness and strategic implications of a parsimonious advertising – inventory competitive model with extensions to pricing competition," International Journal of Production Economics, Elsevier, vol. 180(C), pages 38-47.
    2. Talat S. Genc & Georges Zaccour, 2010. "Investment Dynamics: Good News Principle," Working Papers 1006, University of Guelph, Department of Economics and Finance.
    3. Genc, Talat S., 2017. "The impact of lead time on capital investments," Journal of Economic Dynamics and Control, Elsevier, vol. 82(C), pages 142-164.
    4. Michael Caputo & Chen Ling, 2015. "Intrinsic Comparative Dynamics of Locally Differentiable Feedback Stackelberg Equilibria," Dynamic Games and Applications, Springer, vol. 5(1), pages 1-25, March.
    5. Martín-Herrán, Guiomar & McQuitty, Shaun & Sigué, Simon Pierre, 2012. "Offensive versus defensive marketing: What is the optimal spending allocation?," International Journal of Research in Marketing, Elsevier, vol. 29(2), pages 210-219.
    6. Gary M. Erickson, 2009. "Advertising Competition in a Dynamic Oligopoly with Multiple Brands," Operations Research, INFORMS, vol. 57(5), pages 1106-1113, October.
    7. Genc, Talat S. & De Giovanni, Pietro, 2018. "Optimal return and rebate mechanism in a closed-loop supply chain game," European Journal of Operational Research, Elsevier, vol. 269(2), pages 661-681.
    8. Erickson, Gary M., 2009. "An oligopoly model of dynamic advertising competition," European Journal of Operational Research, Elsevier, vol. 197(1), pages 374-388, August.
    9. Sigué, Simon Pierre & Chintagunta, Pradeep, 2009. "Advertising strategies in a franchise system," European Journal of Operational Research, Elsevier, vol. 198(2), pages 655-665, October.
    10. Fuxiao Lu & Guowei Liu & Jianxiong Zhang & Wansheng Tang, 2016. "Benefits of partial myopia in a durable product supply chain considering pricing and advertising," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(10), pages 1309-1324, October.
    11. Mesak, Hani I. & Bari, Abdullahel & Luehlfing, Michael S. & Han, Fei, 2015. "On modeling the advertising-operations interface under asymmetric competition," European Journal of Operational Research, Elsevier, vol. 240(1), pages 278-291.
    12. Michael P. Atkinson & Moshe Kress & Niall J. MacKay, 2021. "Targeting, Deployment, and Loss-Tolerance in Lanchester Engagements," Operations Research, INFORMS, vol. 69(1), pages 71-81, January.
    13. 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.
    14. Steffen Jørgensen & Georges Zaccour, 2007. "Developments in differential game theory and numerical methods: economic and management applications," Computational Management Science, Springer, vol. 4(2), pages 159-181, April.

    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. Gary M. Erickson, 2009. "Advertising Competition in a Dynamic Oligopoly with Multiple Brands," Operations Research, INFORMS, vol. 57(5), pages 1106-1113, October.
    2. Erickson, Gary M., 2009. "An oligopoly model of dynamic advertising competition," European Journal of Operational Research, Elsevier, vol. 197(1), pages 374-388, August.
    3. 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.
    4. Wang, Qinan & Wu, Zhang, 2007. "An empirical study on the Lanchester model of combat for competitive advertising decisions," European Journal of Operational Research, Elsevier, vol. 183(2), pages 871-881, December.
    5. 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.
    6. Martín-Herrán, Guiomar & McQuitty, Shaun & Sigué, Simon Pierre, 2012. "Offensive versus defensive marketing: What is the optimal spending allocation?," International Journal of Research in Marketing, Elsevier, vol. 29(2), pages 210-219.
    7. Wang, Qinan & Wu, Zhang, 2001. "A duopolistic model of dynamic competitive advertising," European Journal of Operational Research, Elsevier, vol. 128(1), pages 213-226, January.
    8. 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.
    9. El Ouardighi, Fouad & Pasin, Federico, 2006. "Quality improvement and goodwill accumulation in a dynamic duopoly," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1021-1032, December.
    10. Toker Doganoglu & Daniel Klapper, 2006. "Goodwill and dynamic advertising strategies," Quantitative Marketing and Economics (QME), Springer, vol. 4(1), pages 5-29, March.
    11. A. Prasad & S. P. Sethi, 2004. "Competitive Advertising Under Uncertainty: A Stochastic Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 163-185, October.
    12. Prasad A. Naik & Ashutosh Prasad & Suresh P. Sethi, 2008. "Building Brand Awareness in Dynamic Oligopoly Markets," Management Science, INFORMS, vol. 54(1), pages 129-138, January.
    13. Frank M. Bass & Anand Krishnamoorthy & Ashutosh Prasad & Suresh P. Sethi, 2005. "Generic and Brand Advertising Strategies in a Dynamic Duopoly," Marketing Science, INFORMS, vol. 24(4), pages 556-568, February.
    14. 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.
    15. Erickson, Gary M., 1995. "Differential game models of advertising competition," European Journal of Operational Research, Elsevier, vol. 83(3), pages 431-438, June.
    16. Fuxiao Lu & Guowei Liu & Jianxiong Zhang & Wansheng Tang, 2016. "Benefits of partial myopia in a durable product supply chain considering pricing and advertising," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(10), pages 1309-1324, October.
    17. 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.
    18. Miltiadis Chalikias & Michalis Skordoulis, 2017. "Implementation of F.W. Lanchester’s combat model in a supply chain in duopoly: the case of Coca-Cola and Pepsi in Greece," Operational Research, Springer, vol. 17(3), pages 737-745, October.
    19. Guidolin, Mariangela & Guseo, Renato, 2015. "Technological change in the U.S. music industry: Within-product, cross-product and churn effects between competing blockbusters," Technological Forecasting and Social Change, Elsevier, vol. 99(C), pages 35-46.
    20. 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.

    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:inm:ormnsc:v:52:y:2006:i:5:p:804-811. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.