Characterization of synchronization patterns in nonlinear marketing models

Some nonlinear discrete-time dynamic models of marketing competition are used to critically discuss the statement, often made in economic literature, according to which identical agents behave identically and quasi-identical ones behave accordingly. Under this assumption, the whole behavior of interacting agents is summarized by one-dimensional systems, describing the dynamics of so called representative agents. However, even in the simple two-dimensional case, the description in terms of a representative agent may be misleading. This occurs for example when riddling, blowout and other global phenomena related to the existence of measure-theoretic attractors characterize the dynamic scenarios of the full system. To discuss the topic, some results from the theory of dynamical systems and chaos synchronization can be applied.