A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

A stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The propose...

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Main Authors: Jie Ran, Yonghui Zhou
Format: Article
Language:English
Published: Wiley 2024-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2024/6680399
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author Jie Ran
Yonghui Zhou
author_facet Jie Ran
Yonghui Zhou
author_sort Jie Ran
collection DOAJ
description A stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The proposed model’s finite time stability in probability is then investigated using a nonlinear feedback control approach at the interior Nash equilibrium. The stochastic Bellman theory is also used to explore the locally optimum control problem. Furthermore, bifurcation diagrams, time series, and the 0-1 test are used to investigate the chaotic dynamics of this model. Finally, numerical examples are given to illustrate the obtained results.
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institution Kabale University
issn 1099-0526
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spelling doaj-art-2ea52b47700741c18ccde5f8debfad842025-08-20T03:55:07ZengWileyComplexity1099-05262024-01-01202410.1155/2024/6680399A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal ControlJie Ran0Yonghui Zhou1School of Mathematical SciencesSchool of Big Data and Computer ScienceA stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The proposed model’s finite time stability in probability is then investigated using a nonlinear feedback control approach at the interior Nash equilibrium. The stochastic Bellman theory is also used to explore the locally optimum control problem. Furthermore, bifurcation diagrams, time series, and the 0-1 test are used to investigate the chaotic dynamics of this model. Finally, numerical examples are given to illustrate the obtained results.http://dx.doi.org/10.1155/2024/6680399
spellingShingle Jie Ran
Yonghui Zhou
A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control
Complexity
title A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control
title_full A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control
title_fullStr A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control
title_full_unstemmed A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control
title_short A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control
title_sort stochastic discrete fractional cournot duopoly game modeling stability and optimal control
url http://dx.doi.org/10.1155/2024/6680399
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AT yonghuizhou astochasticdiscretefractionalcournotduopolygamemodelingstabilityandoptimalcontrol
AT jieran stochasticdiscretefractionalcournotduopolygamemodelingstabilityandoptimalcontrol
AT yonghuizhou stochasticdiscretefractionalcournotduopolygamemodelingstabilityandoptimalcontrol