A PULSING MODEL OF ADVERTISING COMPETITION - A GAME-THEORETIC APPROACH .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 stati c continuous Lanchester competitive model of two rival firms. The mode ling effort is shown to be adaptable to a wide variety of realistic ri valry situations and its related derived main conclusions are robust f or 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 kn own results for a monopoly to a duopoly. When at least one of the resp onse functions is convex, the study demonstrates that generalizing mon opolistic results might not be adequate. For such situations, the opti mal 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 adve rtising game is solved using linear programming. The Lanchester model is empirically estimated, with considerable success, using the ready-t o-eat cereal data in the US. In the application reported, both respons e functions are found to be linear implying the superiority of UAP for the application reported.