Duopolistic dynamics in markets with competitive advertising and churn

This paper briefly surveys the different models that have been proposed for dynamics of duopolies with competitive advertising and churn. It also proposes a model that is capable of representing competitive advertising and churn, in a unified way for saturated and unsaturated markets. The objective is to carry out a qualitative analysis of the effect of different types of competitive advertising policies in the presence of churn. The proposed model can be seen as a generalization of duopolistic dynamic models that of the classical Vidale-Wolfe and Lanchester type, also including a model of churn. The firm with a perceived lower share of the market switches on an extra control effort in its attempt to get a larger share than its competitor. The main contributions are to show that the proposed approach can serve to explore whether or not it is worth entering a dispute for market share and, if so, what control strategies should be adopted. Furthermore, the effects of churn are studied systematically.