Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand
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 minim...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/6687544 |
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| author | S. S. Askar A. Ibrahim A. A. Elsadany |
| author_facet | S. S. Askar A. Ibrahim A. A. Elsadany |
| author_sort | S. S. Askar |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b370d9c2c79740dfba32c8b2bb770c9b |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b370d9c2c79740dfba32c8b2bb770c9b2025-02-03T01:28:23ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/66875446687544Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic DemandS. S. Askar0A. Ibrahim1A. A. Elsadany2Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh, Saudi ArabiaDepartment of Mathematics and Statistics, School of Quantitative Science, UUM College of Arts and Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, MalaysiaDepartment of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, EgyptA 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.http://dx.doi.org/10.1155/2021/6687544 |
| spellingShingle | S. S. Askar A. Ibrahim A. A. Elsadany Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand Complexity |
| title | Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand |
| title_full | Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand |
| title_fullStr | Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand |
| title_full_unstemmed | Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand |
| title_short | Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand |
| title_sort | dynamics of a heterogeneous constraint profit maximization duopoly model based on an isoelastic demand |
| url | http://dx.doi.org/10.1155/2021/6687544 |
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