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

Sameh Askar
2020 Advances in Difference Equations  
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
more » ... w the dynamic behavior of game's system. We show that the system is noninvertible and belongs to $Z_{2}-Z_{0}$ Z 2 − Z 0 type. We also show some multistability aspects of the system including basins of attraction and regions known as lobes.
doi:10.1186/s13662-020-03144-4 fatcat:6y2hn63dibaf7bzauphgh5zmiq