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Advertising Strategies in a Differential Game with Negative Competitor’s Interference

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  • B. Viscolani

    (University of Padua)

  • G. Zaccour

    (GERAD, HEC Montréal)

Abstract

We consider a duopolistic industry where the current sales of each firm is proportional to its goodwill stock. The evolution of the latter depends positively on own advertising effort and negatively on competitor’s advertising. A standard assumption in the literature in differential games of advertising is that the players remain active throughout the whole (infinite) duration of the game. We relax this assumption and characterize the circumstances under which a firm finds it optimal to remain or exit the industry. Among other things, it is shown that, if both players are “strong”, then the unique Nash equilibrium is the same that one would obtain in the absence of interference from competitor’s advertising.

Suggested Citation

  • B. Viscolani & G. Zaccour, 2009. "Advertising Strategies in a Differential Game with Negative Competitor’s Interference," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 153-170, January.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9454-7
    DOI: 10.1007/s10957-008-9454-7
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    References listed on IDEAS

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    1. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    2. Nawel Amrouche & Guiomar Martín-Herrán & Georges Zaccour, 2008. "Feedback Stackelberg equilibrium strategies when the private label competes with the national brand," Annals of Operations Research, Springer, vol. 164(1), pages 79-95, November.
    3. Nair, Anand & Narasimhan, Ram, 2006. "Dynamics of competing with quality- and advertising-based goodwill," European Journal of Operational Research, Elsevier, vol. 175(1), pages 462-474, November.
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    Cited by:

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