Advertising patterns in a dynamic oligopolistic growing market with decay

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.