Local and global analysis of a nonlinear duopoly game with heterogeneous firms
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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 $Z_{2}-Z_{0}$ Z 2 − Z 0 type. We also show some multistability aspects of the system including basins of attraction and regions known as lobes.
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2009 ◽
Vol 19
(06)
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pp. 2059-2071
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