Nonlinear dynamics of a Cournot duopoly game with differentiated products

• A Cournot duopoly with product differentiation is considered.
• Local stability conditions are provided with respect to the role of product differentiation.
• Neimark–Sacker and flip bifurcation may destabilize the unique Nash equilibrium.
• Global analysis shows attractor coexistence and complex basins’ structure.

In this paper we investigate the dynamics of a Cournot duopoly game with differentiated goods in which boundedly rational firms apply a gradient adjustment mechanism to update the quantity produced in each period. As in Ahmed et al. (2015), the demand functions are derived from an underlying CES utility function. The present analysis reveals that a higher degree of product differentiation may destabilize the Nash equilibrium. Through local analysis we provide conditions for the stability of the market equilibrium and through global analysis we investigate some bifurcations which cause qualitative changes in the structure of the attractors and of their basins as some parameters are allowed to vary. Since a higher degree of product differentiation tends to reduce competition and may generate undesirable fluctuations, an implication of our findings is that a stronger competition could help in stabilizing the unique Nash equilibrium.