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

We develop a nonlinear dynamic Cournot duopoly model, where boundedly rational quantity-setting firms, all endowed with naïve expectations, are heterogeneous as to their cost functions and output strategies. Two types of firms are considered, adopting Best Reply and gradient `behavioral rules', respectively. Increasing values of the adjustment parameter of the latter type of firms may destabilize the Cournot-Nash equilibrium point and bring about complex dynamic scenarios. The nature of such phenomena is strongly dependent on the ratio between firms' marginal costs. The paper also investigates numerically the impact of fixed costs on long-term firms' survival, along different output trajectories.