A pulsing model of advertising competition: A game theoretic approach, part A – Theoretical foundation

In this paper and its sequel, we present a theoretical model supported by both numerical and empirical analyses to evaluate the advertising policies of pulsation versus uniform (constant) spending using a static continuous Lanchester competitive model of two rival firms. The modeling effort is shown to be adaptable to a wide variety of realistic rivalry situations and its related derived main conclusions are robust for a broad set of assumptions. Following a game theoretic approach, it is found that Uniform Advertising Policy (UAP) is optimal for a firm having a concave or linear response function competing against another having a concave or linear response function and thus generalizing known results for a monopoly to a duopoly. When at least one of the response functions is convex, the study demonstrates that generalizing monopolistic results might not be adequate. For such situations, the optimal policy of the firm may involve the Advertising Pulsing/Maintenance Policy (APMP) replacing the monopolistic Advertising Pulsing Policy (APP) optimal when the response function is convex, or the monopolistic UAP optimal when the response function is concave or linear. For the competitive situations involving convex response function(s), the advertising game is solved using linear programming. The Lanchester model is empirically estimated, with considerable success, using the ready-to-eat cereal data in the US. In the application reported, both response functions are found to be linear implying the superiority of UAP for the application reported.