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

Author

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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