On the long-time behavior of a continuous duopoly model with constant conjectural variation

TL;DR

This paper analyzes a continuous duopoly model with constant conjectural variation, demonstrating boundedness and conditions for global stability of solutions using Lyapunov methods.

Contribution

It introduces a continuous ODE-based duopoly model derived from a discrete framework and establishes boundedness and global stability conditions.

Findings

Solutions are ultimately bounded in the phase space.

Conditions for nonlinear, global, asymptotic stability are identified.

Lyapunov methods are used to prove stability.

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 ultimately boundedness of the solutions (existence of an absorbing set in the phase space) is shown and conditions guaranteeing the nonlinear, global, asymptotic stability of solutions have been found using the Liapunov direct method.