On the non-linear stability of a continuous duopoly model with constant conjectural variation. (May 2016)

• Record Type: Journal Article
• Authors: Torcicollo, Isabella
• Is Part Of: International journal of non-linear mechanics. Volume 81(2016)
• Page Start: 268
• Page End: 273
• Publication Date: 2016-05
• Subjects: Non-linear duopoly game -- Conjectural variation model -- Bounded rationality -- Continuous models -- Non-linear stability; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2016.01.018
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: 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. Abstract : Highlights: 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.