An Empirical Investigation of Advertising Strategies in a Dynamic Duopoly

The equilibrium profit-maximizing advertising policies of firms operating in a dynamic duopoly are derived by linking in a single framework the econometric estimation of the market response function and the technique of differential games that characterizes dynamic competitive behavior. We use the Lanchester model of combat to represent the system dynamics that capture the competitive shifts due to investments in advertising by the two market rivals. We determine the equilibrium advertising levels using both closed- and open-loop policies. We also compare these equilibrium advertising policies for each firm to those obtained using an optimal control theory formulation wherein the advertising spending levels of the rival are assumed to be known. The empirical results obtained by analyzing the advertising rivalry between Coke and Pepsi for the period 1968--1981 under the above three alternative spending policies provide some interesting insights into the nature of competition between these two market rivals. A significant contribution of this paper is to extend the existing literature on advertising competition by integrating theoretical and empirical analyses.