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Closed-Loop Advertising Strategies in a Duopoly

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Author Info

  • 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)

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    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.43.1.54
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 43 (1997)
    Issue (Month): 1 (January)
    Pages: 54-63

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    Handle: RePEc:inm:ormnsc:v:43:y:1997:i:1:p:54-63

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    Related research

    Keywords: marketing; competitive strategy; Nash equilibrium; bilinear-quadratic differential game; noncooperative;

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    Citations

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    Cited by:
    1. 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.
    2. 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.
    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. 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.
    5. Matthew Spiegel & Heather Tookes, 2008. "Dynamic Competition, Innovation and Strategic Financing," Yale School of Management Working Papers amz2500, Yale School of Management.
    6. 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.
    7. 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.
    8. 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.

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