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Advertising patterns in a dynamic oligopolistic growing market with decay

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  • Amir, Rabah
  • Machowska, Dominika
  • Troege, Michael

Abstract

A finite-horizon Lanchester model of a (continuous-time) differential game of oligopolistic advertising is considered, and the analytical form of the unique closed-loop Nash equilibrium derived and analyzed. In contrast to previous research, the finite-horizon Lanchester model is modified to include two novel factors. First, a growing market allows us to analyze the competition for a potential market via generic advertising, with the latter giving the otherwise zero-sum-like game a public good dimension. Second, it is assumed that each firm’s market share declines in the absence of advertising efforts. The analysis investigates the Markovian (closed-loop) equilibrium calling for firms operating in a competitive growing market to invest in offensive, defensive or generic advertising in all or part of the decision horizon. In the most novel part of the paper, the non-cooperative outcome is compared to the Pareto-optimal or cooperative solution. The conclusions derived reveal significant differences in the resulting patterns of co-existence of the different dimensions of advertising over time, relative to the existing literature.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:dyncon:v:131:y:2021:i:c:s0165188921001640
    DOI: 10.1016/j.jedc.2021.104229
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    More about this item

    Keywords

    Dynamic oligopoly; Growing market; Market share decay; Lanchester model; Cooperative advertising;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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