Marketing investment decisions in a dynamic duopoly: a model and empirical analysis

Determining the levels of profit-maximizing investments in marketing mix activities such as advertising, detailing and sales promotion in a dynamic competitive environment is an important, but difficult managerial task. In this paper, we model the marketing rivalry over time between two competing firms as a differential game and derive expressions for the equilibrium investment decisions using closed-loop policies. We apply the analytical results derived from our model to examine empirically the dynamic advertising and detailing policies of two competing brands of a prescription drug. Our empirical results show that each firm takes into consideration the actions of its rival when determining its advertising and detailing expenditures. We also find that a firm could be misallocating resources between the different marketing mix instruments, even though the actual total expenditures may be close to the equilibrium levels. This suggests that when firms use multiple marketing mix investments as competitive tools, it could be misleading to model them as a single promotional variable.