Local and global analysis of a nonlinear duopoly game with heterogeneous firms

Abstract

AbstractIn this paper, we introduce a nonlinear duopoly game whose players are heterogeneous and their inverse demand functions are derived from a more general isoelastic demand. The game is modeled by a discrete time dynamic system whose Nash equilibrium point is unique. The conditions of local stability of Nash point are calculated. It becomes unstable via two types of bifurcations: flip and Neimark–Sacker. Some local and global numerical investigations are performed to show the dynamic behavior of game’s system. We show that the system is noninvertible and belongs to$Z_{2}-Z_{0}$Z2−Z0type. We also show some multistability aspects of the system including basins of attraction and regions known as lobes.