Journal
JOURNAL OF ECONOMIC DYNAMICS & CONTROL
Volume 131, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.jedc.2021.104229
Keywords
Dynamic oligopoly; Growing market; Market share decay; Lanchester model; Cooperative advertising
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This study examines a finite-horizon Lanchester model with two novel factors: a growing market and declining market share. Findings show that in a competitive growing market, firms need to invest in different types of advertising for optimal returns, and compares these outcomes to cooperative solutions.
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. (C) 2021 Elsevier B.V. All rights reserved.
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