20.500.12556/DKUM-84868 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 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. nonlinear dynamics game theory stability analysis public goods nelinearna dinamika teorija iger stabilnostna analiza javno dobro true true true Public Library of Science Angleški jezik Slovenski jezik Članek v reviji 2023-08-02 09:53:39 2023-08-02 09:53:39 2024-06-10 08:49:33 0000-00-00 00:00:00 2023 0 0 22 str. iss. 4, article no. e0283757 Vol. 18 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2022-11-11 2023-03-16 2023-04-05 53 148649987 10.1371/journal.pone.0283757 1932-6203 The_dynamics_of_a_duopoly_Stackelb-Ahmadi-2023.pdf The_dynamics_of_a_duopoly_Stackelb-Ahmadi-2023.pdf 1 79C3AF950AEAFA90DAAEEED034A96AD2 1724bc7dc2c13d6280510fdcd9a541da7b9df0f75aa66c61c025355eae8d9076 f771f556-3109-11ee-b6b4-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=169164 https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0283757 0 0226841f-310a-11ee-b6b4-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=169165 Fakulteta za naravoslovje in matematiko 0 0 0