A study of duopolistic dynamics with competitive advertising based on state-dependent switching behavior

This paper explores the effect of different types of competitive advertising policies in duopolistic dynamic models that are variants of the classical Vidale-Wolfe and Lanchester models. 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. An analysis of the dynamics of the proposed policies is carried out, characterizing sets of initial conditions for which different outcomes occur. The main contribution is 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.