In this paper, we investigate the question of whether the assumption of the “representative agent”, often made in economic modeling, is innocuous or whether it may be misleading under certain circumstances. In order to obtain some insight into this question, two dynamic Cournot duopoly games are considered, whose dynamics are represented by discrete-time dynamical systems. For each of these mod...

A standard use of shadowing lemmas in dynamical systems theory is to prove density of periodic points. When there is symmetry present it is natural to investigate the density of periodic points of a given symmetry. We obtain several results in this direction. As an application, we prove a result about compact group extensions of hyperbolic and nonuniformly hyperbolic dynamical systems.