库诺-伯特兰二元垄断模型:基于计算成本的动态分析

IF 1.7 4区 工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Complexity Pub Date : 2024-02-06 DOI:10.1155/2024/5594918
S. S. Askar, Ahmed M. Alshamrani
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引用次数: 0

摘要

本文研究了使用计算非线性成本的库诺-贝特朗二元博弈的一些数学性质和动态研究。博弈是重复的,其演化是通过非可逆映射呈现的。计算了该图的固定点,并讨论了其稳定性条件。其中一个定点是纳什均衡,讨论表明它可能通过翻转和 Neimark-Sacker 分岔而不稳定。分析了博弈图的不变流形。此外,还研究了竞争双方都是独立公司的情况。由于博弈图的非对称结构,全局分析产生了某些吸引集的复杂吸引盆地。这些吸引盆地的拓扑结构表明,某些吸引集的逃逸(不可行)域变得不相连,并出现了洞。这证实了接触分岔的存在。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost

In this paper, some mathematical properties and dynamic investigations of a Cournot–Bertrand duopoly game using a computed nonlinear cost are studied. The game is repeated and its evolution is presented by noninvertible map. The fixed points for this map are calculated and their stability conditions are discussed. One of those fixed points is Nash equilibrium, and the discussion shows that it can be unstable through flip and Neimark–Sacker bifurcation. The invariant manifold for the game’s map is analyzed. Furthermore, the case when both competing firms are independent is investigated. Due to unsymmetrical structure of the game’s map, global analysis gives rise to complicated basin of attraction for some attracting sets. The topological structure for these basins of attraction shows that escaping (infeasible) domain for some attracting sets becomes unconnected and the rise of holes is obtained. This confirms the existence of contact bifurcation.

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来源期刊
Complexity
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.
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