Multistability and path dependence in a dynamic brand competition model

We introduce a dynamic market share attraction model where agents are boundedly rational. They follow a simple rule of thumb which is based on marginal profits to determine their actions over time. We show that multistability arises, i.e. several attractors coexist. In such a situation the selected long run state becomes path-dependent, and a thorough knowledge of the basins and their structure becomes crucial for the researcher to be able to predict the long run outcome of the economic system. We show that the basins of the coexisting attracting sets might have quite complicated structure. Furthermore, we give insights into the mechanism which is responsible for the creation of complex basins of attraction.