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• W4362601075 endingPage "e0283757" @default.
• W4362601075 startingPage "e0283757" @default.
• W4362601075 abstract "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." @default.
• W4362601075 created "2023-04-06" @default.
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• W4362601075 date "2023-04-05" @default.
• W4362601075 modified "2023-09-29" @default.
• W4362601075 title "The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players" @default.
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• W4362601075 doi "https://doi.org/10.1371/journal.pone.0283757" @default.
• W4362601075 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/37018231" @default.
• W4362601075 hasPublicationYear "2023" @default.
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