Dynamic Analysis of a Simple Cournot Duopoly Model Based on a Computed Cost

S. S. Askar, Ahmad M. Alshamrani and Youssef N. Raffoul

Discrete Dynamics in Nature and Society, 2024, vol. 2024, 1-17

Abstract: The paper is organized to study some mathematical properties and dynamics of a simple Cournot duopoly game based on a computed quadratic cost. The time evolution of this game is described by a two-dimensional noninvertible discrete time map using the bounded rationality mechanism. For this map, some dynamic characteristics such as multistability and synchronization are investigated. Its equilibrium points are obtained for the asymmetric case, and their conditions of stability are obtained. Our results investigate that the Nash equilibrium point may be unstable due to flip bifurcation and under certain parameter values, and Neimark–Sacker bifurcation is born after the period-4 cycle. Through some restrictions, the coordinate axes of the map construct an invariant manifold, and therefore, their dynamics can be analyzed by using a one-dimensional map. In the symmetric case, both firms behave identically, and this implies that the diagonal set forms an invariant manifold, and hence the synchronization phenomena take place. Furthermore, the global bifurcation of the map is confirmed through contact between critical curves and the boundaries of infeasible domains.

Date: 2024
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/ddns/2024/9912671.pdf (application/pdf)
http://downloads.hindawi.com/journals/ddns/2024/9912671.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:9912671

DOI: 10.1155/2024/9912671

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().