摘要
由一名新闻记者兼机器人与机器学习的新闻编辑每日新闻-符号计算的新数据在一份新的报告中呈现。根据NewsRx编辑在中国北京的新闻报道，研究表明，“自从Kopel的双寡头模型在大约30年前提出以来，几乎没有关于非对称情况下均衡及其稳定性的分析结果。我们研究的第一个目标是填补这一空白。”本研究经费来自广东省哲学社会科学基金。本文引用了北京航空航天大学的一篇研究文章:“本文利用符号计算的几种工具对Kopel的非对称双寡头模型进行了分析,讨论了存在多个正平衡点的可能性,建立了一定数量的正平衡点存在的条件,并探讨了Kopel模型中Kopel的可能位置。”在Ko Pel的非对称模型中，如果双极主义者采用最佳反应反应或齐次自适应期望，我们首次建立了平衡点局部稳定的条件。通过数值模拟的观测结果似乎支持了Kopel模型中混沌的发生，但严格证明是困难的。
Abstract
By a News Reporter-Staff News Editor at Robotics & Machine Learning Daily News Daily News – Fresh data on Symbolic Computation are presented in a new report. According to news reporting out of Beijing, People’s Republic of China, by NewsRx editors, research stated, “Since Kopel’s duopoly m odel was proposed about 3 decades ago, there are almost no analytical results on the equilibria and their stability in the asymmetric case. The first objective of our study is to fill this gap.” Financial support for this research came from Philosophy and Social Science Foun dation of Guangdong. Our news journalists obtained a quote from the research from Beihang University, “This paper analyzes the asymmetric duopoly model of Kopel analytically by usin g several tools based on symbolic computations.We discuss the possibility of th e existence of multiple positive equilibria and establish conditions for a given number of positive equilibria to exist. The possible positions of the equilibri a in Kopel’s model are also explored. Furthermore, in the asymmetric model of Ko pel, if the duopolists adopt the best response reactions or homogeneous adaptive expectations, we establish conditions for the local stability of equilibria for the first time. The occurrence of chaos in Kopel’s model seems to be supported by observations through numerical simulations, which, however, is challenging to prove rigorously.”
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