Abstract
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.
Highlights
In 1838, Antoine Augustin Cournot introduced the concept of duopoly in his book titled Researches on the Mathematical Principles of the eory of Wealth
Most discrete time oligopoly dynamics that have been considered in the past two decades were based on the single objective of maximizing profit of firms [7,8,9,10]
Work is paper features complex behaviors of heterogeneous Cournot duopoly game in which players optimize their profits under minimal sales constraints
Summary
Received 20 December 2020; Revised February 2021; Accepted March 2021; Published 28 March 2021. 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. A model of constrained profit maximization (CPM) occurs when a business needs to be increased with profit minimal sales constraints. E CPM model, in which companies maximize profits under the minimum sales constraints, is an alternative to the profit maximization model. E current study constructs a duopoly game based on an isoelastic demand and homogeneous goods with heterogeneous strategies. E initial results show that the duopoly model would be easier to stabilize if firms were to impose certain minimum sales constraints. Our findings show that the effect of game parameters on stability depends on the rules of expectations and restriction of sales by firms
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