On the generalizability of advertising pulsation monopoly results to an oligopoly

This paper introduces, for the first time, an analytical framework for modeling and analyzing sales response to advertising pulsation for competitive markets of mature products in continuous time for discrete, piecewise policies that allow unequal cycle lengths. Employing a Nash equilibrium solution concept, this study supported with numerical analysis demonstrates that there is an oligopolistic, as opposed to a monopolistic, justification for advertising at a constant rate in the presence of concave response functions or advertising according to a pulsing policy in the presence of S-shaped response functions. The article employs a modeling framework whereby each of a set of competitors' responses to advertising spending is governed mainly by Lanchester type response and is used to analyze the game resulting from cyclical advertising policies that are strictly adhered to by all players. A non-discounted averaged performance is used to assess the purported optimality of different variants of piecewise-constant policies.