Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games
An N-firm production game known as oligopoly will be examined with isoelastic price function and linear cost under al Cournot competition. After the best responses of the firms are determined, a dynamic system with adaptive expectations is introduced. It is first shown that the local asymptotic beha...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/380530 |
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| author | Akio Matsumoto Ferenc Szidarovszky |
| author_facet | Akio Matsumoto Ferenc Szidarovszky |
| author_sort | Akio Matsumoto |
| collection | DOAJ |
| description | An N-firm production game known as oligopoly will be examined with isoelastic price function and linear cost under al Cournot competition. After the best responses of the firms are determined, a dynamic system with adaptive expectations is introduced. It is first shown that the local asymptotic behavior of the system is identical with that of the adaptive adjustment process in which the firms cautiously determine their outputs. Dynamic analysis is confined to two special cases, one in which
N is divided into two groups and the other in which
N is divided into three groups. Then stability conditions will be derived and the global behavior of the equilibria will be illustrated including chaos control. Lastly the two- and three-group models are compared with two-firm (duopoly) and three-firm (triopoly) models to shed light on roles of the number of the firms. |
| format | Article |
| id | doaj-art-03e548608fd942eea0541c69b44801a4 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-03e548608fd942eea0541c69b44801a42025-08-20T02:03:19ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/380530380530Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot GamesAkio Matsumoto0Ferenc Szidarovszky1Department of Economics, Chuo University, 742-1 Higashi-Nakano, Hachioji, Tokyo 192-0393, JapanDepartment of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721-0020, USAAn N-firm production game known as oligopoly will be examined with isoelastic price function and linear cost under al Cournot competition. After the best responses of the firms are determined, a dynamic system with adaptive expectations is introduced. It is first shown that the local asymptotic behavior of the system is identical with that of the adaptive adjustment process in which the firms cautiously determine their outputs. Dynamic analysis is confined to two special cases, one in which N is divided into two groups and the other in which N is divided into three groups. Then stability conditions will be derived and the global behavior of the equilibria will be illustrated including chaos control. Lastly the two- and three-group models are compared with two-firm (duopoly) and three-firm (triopoly) models to shed light on roles of the number of the firms.http://dx.doi.org/10.1155/2011/380530 |
| spellingShingle | Akio Matsumoto Ferenc Szidarovszky Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games Discrete Dynamics in Nature and Society |
| title | Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games |
| title_full | Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games |
| title_fullStr | Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games |
| title_full_unstemmed | Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games |
| title_short | Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games |
| title_sort | stability bifurcation and chaos in n firm nonlinear cournot games |
| url | http://dx.doi.org/10.1155/2011/380530 |
| work_keys_str_mv | AT akiomatsumoto stabilitybifurcationandchaosinnfirmnonlinearcournotgames AT ferencszidarovszky stabilitybifurcationandchaosinnfirmnonlinearcournotgames |