Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules

Abstract

We develop a nonlinear dynamic Cournot duopoly model in discrete time, where two bounded rational quantity-setting firms, both endowed with naïve expectations, are heterogeneous as to their cost functions and output strategies. One of the two competing firms adopts best-reply behaviour, whereas the other adjusts its production according to the gradient of its profit. Although excessive reaction of the latter firm generally results in destabilization of the ‘Cournot–Nash’ equilibrium and brings about complex dynamic scenarios, this occurs via qualitatively different bifurcation routes, depending on the ratio between firms’ marginal costs. The paper also provides a preliminary exploration of the long-run sustainability of the heterogeneous duopoly competition, by investigating numerically the impact of fixed costs on firms’ survival, along different output trajectories.