The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players.
One of the famous economic models in game theory is the duopoly Stackelberg model, in which a leader and a follower firm manufacture a single product in the market. Their goal is to obtain the maximum profit while competing with each other. The desired dynamics for a firm in a market is the converge...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2023-01-01
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| Series: | PLoS ONE |
| Online Access: | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0283757&type=printable |
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| author | Atefeh Ahmadi Sourav Roy Mahtab Mehrabbeik Dibakar Ghosh Sajad Jafari Matjaž Perc |
| author_facet | Atefeh Ahmadi Sourav Roy Mahtab Mehrabbeik Dibakar Ghosh Sajad Jafari Matjaž Perc |
| author_sort | Atefeh Ahmadi |
| collection | DOAJ |
| description | One of the famous economic models in game theory is the duopoly Stackelberg model, in which a leader and a follower firm manufacture a single product in the market. Their goal is to obtain the maximum profit while competing with each other. The desired dynamics for a firm in a market is the convergence to its Nash equilibrium, but the dynamics of real-world markets are not always steady and can result in unpredictable market changes that exhibit chaotic behaviors. On the other hand, to approach reality more, the two firms in the market can be considered heterogeneous. The leader firm is bounded rationale, and the follower firm is adaptable. Modifying the cost function that affects the firms' profit by adding the marginal cost term is another step toward reality. We propose a Stackelberg model with heterogeneous players and marginal costs, which exhibits chaotic behavior. This model's equilibrium points, including the Nash equilibrium, are calculated by the backward induction method, and their stability analyses are obtained. The influence of changing each model parameter on the consequent dynamics is investigated through one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents spectra, and Kaplan-Yorke dimension. Eventually, using a combination of state feedback and parameter adjustment methods, the chaotic solutions of the model are successfully tamed, and the model converges to its Nash equilibrium. |
| format | Article |
| id | doaj-art-3612ba9d5cc24983aac41f78f6dcd314 |
| institution | DOAJ |
| issn | 1932-6203 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-3612ba9d5cc24983aac41f78f6dcd3142025-08-20T03:13:30ZengPublic Library of Science (PLoS)PLoS ONE1932-62032023-01-01184e028375710.1371/journal.pone.0283757The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players.Atefeh AhmadiSourav RoyMahtab MehrabbeikDibakar GhoshSajad JafariMatjaž PercOne of the famous economic models in game theory is the duopoly Stackelberg model, in which a leader and a follower firm manufacture a single product in the market. Their goal is to obtain the maximum profit while competing with each other. The desired dynamics for a firm in a market is the convergence to its Nash equilibrium, but the dynamics of real-world markets are not always steady and can result in unpredictable market changes that exhibit chaotic behaviors. On the other hand, to approach reality more, the two firms in the market can be considered heterogeneous. The leader firm is bounded rationale, and the follower firm is adaptable. Modifying the cost function that affects the firms' profit by adding the marginal cost term is another step toward reality. We propose a Stackelberg model with heterogeneous players and marginal costs, which exhibits chaotic behavior. This model's equilibrium points, including the Nash equilibrium, are calculated by the backward induction method, and their stability analyses are obtained. The influence of changing each model parameter on the consequent dynamics is investigated through one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents spectra, and Kaplan-Yorke dimension. Eventually, using a combination of state feedback and parameter adjustment methods, the chaotic solutions of the model are successfully tamed, and the model converges to its Nash equilibrium.https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0283757&type=printable |
| spellingShingle | Atefeh Ahmadi Sourav Roy Mahtab Mehrabbeik Dibakar Ghosh Sajad Jafari Matjaž Perc The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players. PLoS ONE |
| title | The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players. |
| title_full | The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players. |
| title_fullStr | The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players. |
| title_full_unstemmed | The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players. |
| title_short | The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players. |
| title_sort | dynamics of a duopoly stackelberg game with marginal costs among heterogeneous players |
| url | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0283757&type=printable |
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