A Bertrand Duopoly Game with Long-Memory Effects
Reconsidering the Bertrand duopoly game based on the concept of long short-term memory, we construct a fractional-order Bertrand duopoly game by extending the integer-order game to its corresponding fractional-order form. We build such a Bertrand duopoly game, in which both players can make their de...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/2924169 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832568516872503296 |
|---|---|
| author | Baogui Xin Fangrui Cao Wei Peng Abdelalim A. Elsadany |
| author_facet | Baogui Xin Fangrui Cao Wei Peng Abdelalim A. Elsadany |
| author_sort | Baogui Xin |
| collection | DOAJ |
| description | Reconsidering the Bertrand duopoly game based on the concept of long short-term memory, we construct a fractional-order Bertrand duopoly game by extending the integer-order game to its corresponding fractional-order form. We build such a Bertrand duopoly game, in which both players can make their decisions with long-memory effects. Then, we investigate its Nash equilibria, local stability, and numerical solutions. Using the bifurcation diagram, the phase portrait, time series, and the 0-1 test for chaos, we numerically validate these results and illustrate its complex phenomena, such as bifurcation and chaos. |
| format | Article |
| id | doaj-art-a79c8a521d2a48f7ac63e9690b03f18a |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-a79c8a521d2a48f7ac63e9690b03f18a2025-02-03T00:58:57ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/29241692924169A Bertrand Duopoly Game with Long-Memory EffectsBaogui Xin0Fangrui Cao1Wei Peng2Abdelalim A. Elsadany3School of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, ChinaSchool of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, ChinaSchool of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, ChinaDepartment of Mathematics, College of Sciences and Humanities Studies in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaReconsidering the Bertrand duopoly game based on the concept of long short-term memory, we construct a fractional-order Bertrand duopoly game by extending the integer-order game to its corresponding fractional-order form. We build such a Bertrand duopoly game, in which both players can make their decisions with long-memory effects. Then, we investigate its Nash equilibria, local stability, and numerical solutions. Using the bifurcation diagram, the phase portrait, time series, and the 0-1 test for chaos, we numerically validate these results and illustrate its complex phenomena, such as bifurcation and chaos.http://dx.doi.org/10.1155/2020/2924169 |
| spellingShingle | Baogui Xin Fangrui Cao Wei Peng Abdelalim A. Elsadany A Bertrand Duopoly Game with Long-Memory Effects Complexity |
| title | A Bertrand Duopoly Game with Long-Memory Effects |
| title_full | A Bertrand Duopoly Game with Long-Memory Effects |
| title_fullStr | A Bertrand Duopoly Game with Long-Memory Effects |
| title_full_unstemmed | A Bertrand Duopoly Game with Long-Memory Effects |
| title_short | A Bertrand Duopoly Game with Long-Memory Effects |
| title_sort | bertrand duopoly game with long memory effects |
| url | http://dx.doi.org/10.1155/2020/2924169 |
| work_keys_str_mv | AT baoguixin abertrandduopolygamewithlongmemoryeffects AT fangruicao abertrandduopolygamewithlongmemoryeffects AT weipeng abertrandduopolygamewithlongmemoryeffects AT abdelalimaelsadany abertrandduopolygamewithlongmemoryeffects AT baoguixin bertrandduopolygamewithlongmemoryeffects AT fangruicao bertrandduopolygamewithlongmemoryeffects AT weipeng bertrandduopolygamewithlongmemoryeffects AT abdelalimaelsadany bertrandduopolygamewithlongmemoryeffects |