On New Phenomena in Dynamic Promotional Competition Models with Homogeneous and Quasi-homogeneous Firms

In this paper we study a class of dynamic promotional competition models, in which firms compete for market share by expending marketing effort. We investigate two main issues. First, we answer the question if it is possible to give a global characterization of the stability of the steady state effort allocation. We show that by using the concept of critical curves and an invariance property of the coordinate axes a characterization of the set of feasible points (points that generate positive trajectories converging to the steady state allocation) and its changes can be given. Second, we deal with the assumption of homogeneous firms, which is often made in the literature. We demonstrate that the symmetric model which derives from this assumption exhibits, in many situations, non-generic dynamical behavior. New phenomena, like Milnor attractors and synchronization of trajectories, arising in the homogeneous case are illustrated. The introduction of small heterogeneities into the model invalidates many of the conclusions derived under the hypothesis of homogeneous firms.