Periodic Advertising Pulsing in a Competitive Market

The question as to the optimality of advertising pulsing has attracted many researchers since first posed by Vidale and Wolfe (1957). In this paper we specify a market share model in which there are two advertising setting firms as well as a no purchase state. The framework is one of a first order Markov process with three states. When the second brand is eliminated the framework collapses to exactly the discrete analog of the Vidale and Wolfe model. The objective of both firms is to maximize profits and a Nash equilibrium is sought. We are able to demonstrate, for a diminishing returns advertising function that the optimal advertising strategy is pulsing. The frequency of the advertising pulse is shown to depend on the magnitude of the market share retention rate (state dependence); the higher it is the less frequent the advertising. We further find that the optimal advertising budgets do not remain the same when the frequency of pulsing changes. Finally, we show that it is optimal for both firms to advertise in-phase