Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare
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...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/6697341 |
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| _version_ | 1850165749659729920 |
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| author | S. S. Askar A. A. Elsadany |
| author_facet | S. S. Askar A. A. Elsadany |
| author_sort | S. S. Askar |
| collection | DOAJ |
| description | 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 Z4−Z2. |
| format | Article |
| id | doaj-art-eace066a8a894b78b17b3ce3acb7a547 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-eace066a8a894b78b17b3ce3acb7a5472025-08-20T02:21:39ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/66973416697341Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social WelfareS. S. Askar0A. A. Elsadany1Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh, Saudi ArabiaDepartment of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, EgyptIn 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 Z4−Z2.http://dx.doi.org/10.1155/2021/6697341 |
| spellingShingle | S. S. Askar A. A. Elsadany Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare Discrete Dynamics in Nature and Society |
| title | Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare |
| title_full | Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare |
| title_fullStr | Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare |
| title_full_unstemmed | Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare |
| title_short | Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare |
| title_sort | nonlinear dynamics of cournot duopoly game when one firm considers social welfare |
| url | http://dx.doi.org/10.1155/2021/6697341 |
| work_keys_str_mv | AT ssaskar nonlineardynamicsofcournotduopolygamewhenonefirmconsiderssocialwelfare AT aaelsadany nonlineardynamicsofcournotduopolygamewhenonefirmconsiderssocialwelfare |