Nonlinear dynamic and chaos in a remanufacturing duopoly game with heterogeneous players and nonlinear inverse demand functions

Abstract

The purpose of this paper is to investigate the dynamics of a remanufacturing duopoly game model with heterogeneous players and different competition strategies, assuming that the original equipment manufacturer has bounded rationality and aims to maximize profit, and the third-party remanufacturer has an adaptive nature and aims to maximize share in order to get a certain profit. The model behaviours are discussed mainly from the point of view of stability, bifurcations and chaos. By utilizing Jury's stability criteria, the Cournot-Nash equilibrium's asymptotic stability is examined. We found that under certain conditions, when consumer willingness to pay was taken as a bifurcation parameter, the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation. Lyapunov exponents are used to demonstrate that the system becomes chaotic through each of the previous bifurcations.

Keywords:

• Discrete dynamical systems
• remanufacturing
• competition strategy
• heterogeneous players
• Chaos

AMS SUBJECT CLASSIFICATIONs:

• 39A23
• 39A28
• 39A30
• 39A33
• 39A60

Disclosure statement

No potential conflict of interest was reported by the author(s).