Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost
In this paper, some mathematical properties and dynamic investigations of a Cournot–Bertrand duopoly game using a computed nonlinear cost are studied. The game is repeated and its evolution is presented by noninvertible map. The fixed points for this map are calculated and their stability conditions...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2024/5594918 |
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| _version_ | 1832545253951799296 |
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| author | S. S. Askar Ahmed M. Alshamrani |
| author_facet | S. S. Askar Ahmed M. Alshamrani |
| author_sort | S. S. Askar |
| collection | DOAJ |
| description | In this paper, some mathematical properties and dynamic investigations of a Cournot–Bertrand duopoly game using a computed nonlinear cost are studied. The game is repeated and its evolution is presented by noninvertible map. The fixed points for this map are calculated and their stability conditions are discussed. One of those fixed points is Nash equilibrium, and the discussion shows that it can be unstable through flip and Neimark–Sacker bifurcation. The invariant manifold for the game’s map is analyzed. Furthermore, the case when both competing firms are independent is investigated. Due to unsymmetrical structure of the game’s map, global analysis gives rise to complicated basin of attraction for some attracting sets. The topological structure for these basins of attraction shows that escaping (infeasible) domain for some attracting sets becomes unconnected and the rise of holes is obtained. This confirms the existence of contact bifurcation. |
| format | Article |
| id | doaj-art-a34a3e4d57f34dde917f90a8c3e96bc5 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-a34a3e4d57f34dde917f90a8c3e96bc52025-02-03T07:26:21ZengWileyComplexity1099-05262024-01-01202410.1155/2024/5594918Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed CostS. S. Askar0Ahmed M. Alshamrani1Department of Statistics and Operations Research College of ScienceDepartment of Statistics and Operations Research College of ScienceIn this paper, some mathematical properties and dynamic investigations of a Cournot–Bertrand duopoly game using a computed nonlinear cost are studied. The game is repeated and its evolution is presented by noninvertible map. The fixed points for this map are calculated and their stability conditions are discussed. One of those fixed points is Nash equilibrium, and the discussion shows that it can be unstable through flip and Neimark–Sacker bifurcation. The invariant manifold for the game’s map is analyzed. Furthermore, the case when both competing firms are independent is investigated. Due to unsymmetrical structure of the game’s map, global analysis gives rise to complicated basin of attraction for some attracting sets. The topological structure for these basins of attraction shows that escaping (infeasible) domain for some attracting sets becomes unconnected and the rise of holes is obtained. This confirms the existence of contact bifurcation.http://dx.doi.org/10.1155/2024/5594918 |
| spellingShingle | S. S. Askar Ahmed M. Alshamrani Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost Complexity |
| title | Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost |
| title_full | Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost |
| title_fullStr | Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost |
| title_full_unstemmed | Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost |
| title_short | Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost |
| title_sort | cournot bertrand duopoly model dynamic analysis based on a computed cost |
| url | http://dx.doi.org/10.1155/2024/5594918 |
| work_keys_str_mv | AT ssaskar cournotbertrandduopolymodeldynamicanalysisbasedonacomputedcost AT ahmedmalshamrani cournotbertrandduopolymodeldynamicanalysisbasedonacomputedcost |