Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization

2021 ◽  
Vol 146 ◽  
pp. 110936
Author(s):  
Hui Li ◽  
Wei Zhou ◽  
A. A Elsadany ◽  
Tong Chu
Keyword(s):  
Profit Maximization ◽  
Spillover Effects ◽  
Knowledge Spillover ◽  
Cournot Duopoly ◽  
Stability And Instability ◽  
Relative Profit

scholarly journals Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
S. S. Askar ◽  
A. Ibrahim ◽  
A. A. Elsadany
Keyword(s):  
Basin Of Attraction ◽  
Profit Maximization ◽  
Period Doubling ◽  
Chaotic Attractors ◽  
Cournot Duopoly ◽  
Coexistence Of Attractors ◽  
Duopoly Model ◽  
Periodic Attractors ◽  
Initial Results ◽  
The Basin Of Attraction

A Cournot duopoly game is a two-firm market where the aim is to maximize profits. It is rational for every company to maximize its profits with minimal sales constraints. As a consequence, a model of constrained profit maximization (CPM) occurs when a business needs to be increased with profit minimal sales constraints. The CPM model, in which companies maximize profits under the minimum sales constraints, is an alternative to the profit maximization model. The current study constructs a duopoly game based on an isoelastic demand and homogeneous goods with heterogeneous strategies. In the event of sales constraint and no sales constraint, the local stability conditions of the Cournot equilibrium are derived. The initial results show that the duopoly model would be easier to stabilize if firms were to impose certain minimum sales constraints. Two routes to chaos are analyzed by numerical simulation using 2D bifurcation diagram, one of which is period doubling bifurcation and the other is Neimark–Sacker bifurcation. Four forms of coexistence of attractors are demonstrated by the basin of attraction, which is the coexistence of periodic attractors and chaotic attractors, the coexistence of periodic attractors and quasiperiodic attractors, and the coexistence of several chaotic attractors. Our findings show that the effect of game parameters on stability depends on the rules of expectations and restriction of sales by firms.

Sign in / Sign up

Export Citation Format

Share Document