A Cournot duopoly game with heterogeneous players: Nonlinear dynamics of the gradient rule versus local monopolistic approach

We analyze a duopolistic Cournotian game with firms producing a homogeneous good, isoelastic demand function and linear total cost functions. In this economic setting, the traditional dynamic adjustment based on the classical best reply mechanism is very demanding in terms of rationality and information set. Therefore, in the competition we study, both the players adopt decisional mechanisms which are based on a reduced degree of rationality, being the agents supposed to have only limited informational and computational capabilities. We assume that the first player adopts a gradient rule mechanism, while the second one adjusts his output level according to a Local Monopolistic Approximation. We provide local stability conditions in terms of marginal costs ratio and complex dynamics are investigated. In particular, we show that two different routes to complicated dynamics are possible: a cascade of flip bifurcations leading to periodic cycles (and chaos) and the Neimark-Sacker bifurcation, which results in an attractive invariant closed curve.