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Markov Perfect Equilibrium Advertising Strategies of Lanchester Duopoly Model: A Technical Note

Author

Listed:
  • Ramla Jarrar

    (GERAD and HEC Montréal, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Québec, H3T 2A7 Canada)

  • Guiomar Martín-Herrán

    (Universidad de Valladolid, Avenida Valle Esgueva, 6, 47011 Valladolid, Spain)

  • Georges Zaccour

    (GERAD and HEC Montréal, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Québec, H3T 2A7 Canada)

Abstract

We propose a numerical approach to compute stationary Markov perfect Nash equilibrium advertising strategies of the Lanchester model. The algorithm can be implemented using a standard mathematical package, and, importantly, it does not require that the players discount their future earnings at a zero rate, an assumption that has been made in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:7:p:995-1000
    DOI: 10.1287/mnsc.1040.0249
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    References listed on IDEAS

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    1. Erickson, Gary M., 1995. "Differential game models of advertising competition," European Journal of Operational Research, Elsevier, vol. 83(3), pages 431-438, June.
    2. Gary M. Erickson, 1992. "Empirical Analysis of Closed-Loop Duopoly Advertising Strategies," Management Science, INFORMS, vol. 38(12), pages 1732-1749, December.
    3. 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.
    4. Gila E. Fruchter & Shlomo Kalish, 1997. "Closed-Loop Advertising Strategies in a Duopoly," Management Science, INFORMS, vol. 43(1), pages 54-63, January.
    5. Gila E. Fruchter, 2001. "Advertising In A Competitive Product Line," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 301-314.
    6. 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.
    7. Gary M. Erickson, 1997. "Note: Dynamic Conjectural Variations in a Lanchester Oligopoly," Management Science, INFORMS, vol. 43(11), pages 1603-1608, November.
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    Cited by:

    1. 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.
    2. Engelbert J. Dockner & Steffen Jørgensen, 2018. "Strategic Rivalry for Market Share: A Contest Theory Approach to Dynamic Advertising Competition," Dynamic Games and Applications, Springer, vol. 8(3), pages 468-489, September.
    3. 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.
    4. 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.
    5. Yuewen Liu & Juan Feng, 2021. "Does Money Talk? The Impact of Monetary Incentives on User-Generated Content Contributions," Information Systems Research, INFORMS, vol. 32(2), pages 394-409, June.
    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. 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.
    8. Malcolm Brady, 2022. "Asymmetric Horizontal Differentiation under Advertising in a Cournot Duopoly," Games, MDPI, vol. 13(3), pages 1-14, May.
    9. 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.
    10. 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.
    11. Erickson, Gary M., 2009. "An oligopoly model of dynamic advertising competition," European Journal of Operational Research, Elsevier, vol. 197(1), pages 374-388, August.
    12. Chaolin Yang & Liang Guo & Sean X. Zhou, 2022. "Customer Satisfaction, Advertising Competition, and Platform Performance," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1576-1594, April.
    13. 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.
    14. 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.

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