On the non-linear stability of a continuous duopoly model with constant conjectural variation

• We propose a generalization of the discrete duopoly model with bounded rationality, based on constant conjectural variation, via a continuous model governed by an ODE system.
• General properties, such as the existence of an absorbing set in the phase space and uniqueness of the solution are obtained.
• The linear stability analysis of the critical points of the system and the non-linear global asymptotic stability of equilibrium of constant conjectural variation are obtained.

The paper concerns a continuous model governed by a ODE system originated by a discrete duopoly model with bounded rationality, based on constant conjectural variation. The aim of this paper is to show (i) the existence of an absorbing set in the phase space; (ii) linear stability analysis of the critical points of the system; (iii) non-linear, global asymptotic stability of equilibrium of constant conjectural variation.