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Closed-Loop Advertising Strategies in a Duopoly

Author

Listed:
  • Gila E. Fruchter

    (Faculty of Industrial Engineering and Management, Technion, Haifa 32000, Israel)

  • Shlomo Kalish

    (The Leon Recanati Graduate School of Business Administration, Tel Aviv University, Tel Aviv 69978, Israel)

Abstract

Using the Lanchester model to describe the dynamics of the market where two firms compete for customers by advertising, we solve the problem of determining an optimal advertising strategy for maximum discounted profits. We develop both open- and closed-loop strategies and explain the relationship between them. Using a new mathematical approach, we prove that our closed-loop solution is a global Nash equilibrium. The closed-loop strategy is time-variant and depends linearly on the actual market share. The time-variant coefficient incorporates the discount factor, its computation requires the solution of a backward differential equation and a set of two nonlinear differential equations for an initial value problem. The closed-loop advertising expenditures are proportional to the open-loop advertising expenditures and to the square of the competitor's actual market share. This provides a very practical adaptive control rule that allows the manager to adjust the actual advertising expenditure and to deviate from budget. We illustrate the use of our control rule, using data for the period 1968--1984 of the Cola War Marketing implications of the results are provided.

Suggested Citation

  • Gila E. Fruchter & Shlomo Kalish, 1997. "Closed-Loop Advertising Strategies in a Duopoly," Management Science, INFORMS, vol. 43(1), pages 54-63, January.
  • Handle: RePEc:inm:ormnsc:v:43:y:1997:i:1:p:54-63
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    File URL: http://dx.doi.org/10.1287/mnsc.43.1.54
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    Citations

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    Cited by:

    1. 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.
    2. Dung Nguyen & Lei Shi, 2006. "Competitive Advertising Strategies and Market-Size Dynamics: A Research Note on Theory and Evidence," Management Science, INFORMS, vol. 52(6), pages 965-973, June.
    3. Nativi, Juan Jose & Lee, Seokcheon, 2012. "Impact of RFID information-sharing strategies on a decentralized supply chain with reverse logistics operations," International Journal of Production Economics, Elsevier, vol. 136(2), pages 366-377.
    4. Fruchter, Gila E., 2001. "A dual control problem and application to marketing," European Journal of Operational Research, Elsevier, vol. 130(1), pages 99-110, April.
    5. 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.
    6. repec:eee:dyncon:v:82:y:2017:i:c:p:142-164 is not listed on IDEAS
    7. Matthew Spiegel & Heather Tookes, 2008. "Dynamic Competition, Innovation and Strategic Financing," Yale School of Management Working Papers amz2500, Yale School of Management.
    8. Marshall Freimer & Dan Horsky, 2012. "Periodic Advertising Pulsing in a Competitive Market," Marketing Science, INFORMS, vol. 31(4), pages 637-648, July.
    9. Yoau-Chau Jeng & Fei-Rung Chiu, 2010. "Allocation model for theme park advertising budget," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(2), pages 333-343, February.
    10. Esther Gal-Or & Mordechai Gal-Or, 2005. "Customized Advertising via a Common Media Distributor," Marketing Science, INFORMS, vol. 24(2), pages 241-253, July.
    11. 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.
    12. Lu, Jye-Chyi & Tsao, Yu-Chung & Charoensiriwath, Chayakrit & Dong, Ming, 2012. "Dynamic decision-making in a two-stage supply chain with repeated transactions," International Journal of Production Economics, Elsevier, vol. 137(2), pages 211-225.
    13. Alex Coram, 2008. "The dynamics of resource spending in a competition between political parties: general notes on the Red Queen effect," UMASS Amherst Economics Working Papers 2008-01, University of Massachusetts Amherst, Department of Economics.
    14. 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.
    15. Erickson, Gary M., 2009. "An oligopoly model of dynamic advertising competition," European Journal of Operational Research, Elsevier, vol. 197(1), pages 374-388, August.
    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. 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.
    18. 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.
    19. Anthony Dukes & Esther Gal–Or, 2003. "Negotiations and Exclusivity Contracts for Advertising," Marketing Science, INFORMS, vol. 22(2), pages 222-245, November.
    20. 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.
    21. 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.
    22. R. Canan Savaskan & Shantanu Bhattacharya & Luk N. Van Wassenhove, 2004. "Closed-Loop Supply Chain Models with Product Remanufacturing," Management Science, INFORMS, vol. 50(2), pages 239-252, February.
    23. 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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