scholarly journals Nonlinear dynamics and global analysis of a heterogeneous Cournot duopoly with a local monopolistic approach versus a gradient rule with endogenous reactivity

2015 ◽  
Vol 23 (1-3) ◽  
pp. 245-262 ◽  
Author(s):  
Fausto Cavalli ◽  
Ahmad Naimzada ◽  
Fabio Tramontana
Keyword(s):  
Nonlinear Dynamics ◽  
Global Analysis ◽  
Cournot Duopoly

scholarly journals Nonlinear dynamics in a Cournot duopoly with relative profit delegation

2012 ◽  
Vol 45 (12) ◽  
pp. 1469-1478 ◽  
Author(s):  
Luciano Fanti ◽  
Luca Gori ◽  
Mauro Sodini
Keyword(s):  
Nonlinear Dynamics ◽  
Cournot Duopoly ◽  
Relative Profit

scholarly journals On Dynamic Investigations of Cournot Duopoly Game: When Firms Want to Maximize Their Relative Profits

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2235
Author(s):  
Sameh Askar
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Utility Function ◽  
Global Analysis ◽  
Asymmetric Structure ◽  
Two Dimensional ◽  
Cournot Duopoly ◽  
The Stability ◽  
Nash Point ◽  
Discrete Map

This paper studies a Cournot duopoly game in which firms produce homogeneous goods and adopt a bounded rationality rule for updating productions. The firms are characterized by an isoelastic demand that is derived from a simple quadratic utility function with linear total costs. The two competing firms in this game seek the optimal quantities of their production by maximizing their relative profits. The model describing the game’s evolution is a two-dimensional nonlinear discrete map and has only one equilibrium point, which is a Nash point. The stability of this point is discussed and it is found that it loses its stability by two different ways, through flip and Neimark–Sacker bifurcations. Because of the asymmetric structure of the map due to different parameters, we show by means of global analysis and numerical simulation that the nonlinear, noninvertible map describing the game’s evolution can give rise to many important coexisting stable attractors (multistability). Analytically, some investigations are performed and prove the existence of areas known in literature with lobes.

scholarly journals Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
S. S. Askar ◽  
A. A. Elsadany
Keyword(s):  
Nonlinear Dynamics ◽  
Social Welfare ◽  
Fixed Points ◽  
Phase Plane ◽  
Complex Dynamics ◽  
Stability Conditions ◽  
Cournot Duopoly ◽  
Discrete Dynamic ◽  
Gradient Based ◽  
Dynamic Map

In this paper, we study the competition between two firms whose outputs are quantities. The first firm considers maximization of its profit while the second firm considers maximization of its social welfare. Adopting a gradient-based mechanism, we introduce a nonlinear discrete dynamic map which is used to describe the dynamics of this game. For this map, the fixed points are calculated and their stability conditions are analyzed. This includes investigating some attracting set and chaotic behaviors for the complex dynamics of the map. We have also investigated the types of the preimages that characterize the phase plane of the map and conclude that the game’s map is noninvertible of type Z 4 − Z 2 .

Global Analysis of Nonlinear Dynamics

2018 ◽  
pp. 203-210
Author(s):  
Jian-Qiao Sun ◽  
Fu-Rui Xiong ◽  
Oliver Schütze ◽  
Carlos Hernández
Keyword(s):  
Nonlinear Dynamics ◽  
Global Analysis
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