A Remanufacturing Duopoly Game Based on a Piecewise Nonlinear Map: Analysis and Investigations

Abstract

Abstract A remanufacturing Cournot duopoly game is introduced based on a nonlinear utility function in this paper. What we mean by remanufacturing here is that the second firm in this game receives used products and remanufacture them and then sell them again in the market. The bounded rationality mechanism is used to form a piecewise system that describes this game in discrete time periods. This piecewise system depends on five parameters and is defined on two regions separated by a border curve. The fixed points of this system in each region are calculated and their stability is discussed. Numerical simulations for this system exhibit the occurrence of different types of multiple attractors. We also give examples of different stable periodic cycles and chaotic attractors that are separated by the border curve or passing through it.