Advertising competition with market expansion for finite horizon firms

Firms that want to increase the sales of their brands through advertising have the choice of capturing market share from their competitors through brand advertising, or increasing primary demand for the category through generic advertising. In this paper, differential game theory is used to analyze the effects of the two types of advertising decisions made by firms offering a product in a dynamic duopoly. Each firm's sales depend not only on its own and its competitor's brand advertising strategies, but also on the generic advertising expenditures of the two firms. Closed-loop Nash equilibrium solutions are obtained for symmetric and asymmetric competitors in a finite-horizon setting. The analysis for the symmetric case results in explicit solutions, and numerical techniques are employed to solve the problem for asymmetric firms.