Synchronization and On-Off Intermittency Phenomena in a Market Model with Complementary Goods and Adaptive Expectations

In this paper we point out some features of the dynamical models describing the interaction of two similar agents competing in a market. Such models are fitted by a two-dimensional map symmetric with respect to the diagonal, i.e., such that M(x,y)= M(y,x). In particular we shall consider a model describing the strategic behavior of two firms that produce complementary goods and have adaptive expectations. The aim of the paper is the analysis of the trajectories generated by the iteration of M starting from different initial conditions. In particular we are interested in two different problems arising in such a situation. First, we analyze the conditions that allow an agent to reach a favourable position (in terms of its profit) in the long run. Second we investigate the mechanisms that lead the agents to behave in the same way in the long run (synchronization) and the phenomena associated with these particular situations, such as the on-off intermittency.