This chapter describes some properties of the nonlinear dynamics emerging from two oligopoly models in discrete time. The target of this chapter is the investigation of some local and global bifurcations which are responsible for the changes in the qualitative behaviors of the trajectories of discrete dynamical systems.Two different kinds of oligopoly models are considered: the first one deals with the presence of differentiated goods and gradient adjustment mechanism, while the second considers the demand function of the producers to be dependent on advertising expenditures and adaptive adjustment of themoves. In bothmodels the standard local stability analysis of the Cournot-Nash equilibrium points is performed, as well as the global bifurcations of both attractors and (their) basins of attraction are investigated.
Agliari, A., Pecora, N., Szuz, A., Dynamical Analysis of Cournot Oligopoly Models: Neimark-Sacker bifurcation and related mechanisms, in G.I. Bischi, A. P. D. R. (ed.), Qualitative Theory of Dynamical Systems, Tools and Applications for Economic Modelling, Springer, Basel 2016: <<SPRINGER PROCEEDINGS IN COMPLEXITY>>, 187- 211. 10.1007/978-3-319-33276-5_3 [http://hdl.handle.net/10807/99907]
Dynamical Analysis of Cournot Oligopoly Models: Neimark-Sacker bifurcation and related mechanisms
Agliari, Anna;Pecora, Nicolo';
2016
Abstract
This chapter describes some properties of the nonlinear dynamics emerging from two oligopoly models in discrete time. The target of this chapter is the investigation of some local and global bifurcations which are responsible for the changes in the qualitative behaviors of the trajectories of discrete dynamical systems.Two different kinds of oligopoly models are considered: the first one deals with the presence of differentiated goods and gradient adjustment mechanism, while the second considers the demand function of the producers to be dependent on advertising expenditures and adaptive adjustment of themoves. In bothmodels the standard local stability analysis of the Cournot-Nash equilibrium points is performed, as well as the global bifurcations of both attractors and (their) basins of attraction are investigated.
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