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

IF 1.7 4区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Complexity Pub Date : 2024-02-09 DOI:10.1155/2024/6680399

Jie Ran, Yonghui Zhou

引用次数: 0

Abstract

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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随机离散分数库诺二元垄断博弈：建模、稳定性和最优控制

本研究建立了一个具有唯一内部纳什均衡的随机离散分数库诺二元博弈模型。利用 Lyapunov 理论推导出了所提模型在内部纳什均衡时概率 Lyapunov 稳定性的一些充分条件。然后利用非线性反馈控制方法研究了所提模型在内部纳什均衡时的有限时间概率稳定性。随机贝尔曼理论也被用来探索局部最优控制问题。此外，还利用分岔图、时间序列和 0-1 检验来研究该模型的混沌动力学。最后，还给出了数值示例来说明所获得的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Complexity 综合性期刊-数学跨学科应用

CiteScore

5.80

自引率

4.30%

发文量

595

审稿时长

>12 weeks

期刊介绍： Complexity is a cross-disciplinary journal focusing on the rapidly expanding science of complex adaptive systems. The purpose of the journal is to advance the science of complexity. Articles may deal with such methodological themes as chaos, genetic algorithms, cellular automata, neural networks, and evolutionary game theory. Papers treating applications in any area of natural science or human endeavor are welcome, and especially encouraged are papers integrating conceptual themes and applications that cross traditional disciplinary boundaries. Complexity is not meant to serve as a forum for speculation and vague analogies between words like “chaos,” “self-organization,” and “emergence” that are often used in completely different ways in science and in daily life.