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Strategic Rivalry for Market Share: A Contest Theory Approach to Dynamic Advertising Competition

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  • Engelbert J. Dockner

    (Vienna University of Economics and Business Administration)

  • Steffen Jørgensen

    (University of Southern Denmark)

Abstract

The paper extends the Lanchester model of advertising competition to a setup in which the rate at which a firm attracts customers from its competitors depends not only on the firm’s own advertising effort, but also on the efforts of its rivals. Doing so enables us to use attraction rate specifications borrowed from the economic theory of contests. Exploiting the fact that the sum of attraction rates equals one, we show that the differential equations that define the evolution of market shares in the Lanchester model can be considerably simplified. This makes the optimization problems of the firms considerably easier to analyze. Finallly, to illustrate how the above extensions work, three alternative specifications of attraction rates are studied: the Tullock ratio formulation, a linear transformation of the Tullock ratio, and a specification that incorporates an exogenous bias.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:3:d:10.1007_s13235-018-0242-1
    DOI: 10.1007/s13235-018-0242-1
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    References listed on IDEAS

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    Cited by:

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    2. Steffen Jørgensen & Ngo Long & Gerhard Sorger, 2018. "Preface: Special issue of Dynamic Games and Applications in Memory of Professor Engelbert J. Dockner," Dynamic Games and Applications, Springer, vol. 8(3), pages 457-467, September.
    3. Natalya Yu. Yaroshevich, 2020. "Enterprises’ competitive behaviour assessment in industrial markets in manufacturing," Journal of New Economy, Ural State University of Economics, vol. 21(2), pages 96-111, July.
    4. Crettez, Bertrand & Hayek, Naila & Zaccour, Georges, 2020. "Do charities spend more on their social programs when they cooperate than when they compete?," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1055-1063.
    5. Amir, Rabah & Machowska, Dominika & Troege, Michael, 2021. "Advertising patterns in a dynamic oligopolistic growing market with decay," Journal of Economic Dynamics and Control, Elsevier, vol. 131(C).

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