 On Complex Dynamics of Differentiated Products: Cournot Duopoly Model under Average Profit MaximizationS.S. Askar and Lei Xie Discrete Dynamics in Nature and Society, 2022, vol. 2022, 1-14 Abstract: In this paper, some important dynamic characteristics such as multistability and synchronization phenomena are investigated for a game of an economic Cournot duopoly whose time evolution is received by the iteration of a noninvertible map in the plane. In the asymmetric case, the equilibrium points of game’s map are calculated, and their stability conditions are obtained. The obtained results show that the Nash equilibrium point loses its stability through flip bifurcation. Under some restrictions, the map’s coordinate axes form an invariant manifold, and hence their dynamics are studied based on a one-dimensional discrete dynamic map. In the symmetric case where both firms are identical, the map has the property of symmetry, and this implies that the diagonal q1=q2 forms an invariant manifold and therefore synchronization phenomena occur. Global analysis of the behavior of the noninvertible map is carried out through studying critical manifolds of the map that categorize it as Z4−Z2−Z0 type. Furthermore, global bifurcation of the basins of attraction is confirmed through contact between the critical curves and the boundaries of escaping domain. Date: 2022 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:8677470 DOI: 10.1155/2022/8677470 Access Statistics for this article More articles in Discrete Dynamics in Nature and Society from Hindawi |
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