This paper is intended to investigate the dynamics of heterogeneous Cournot duopoly games, where the first players adopt identical gradient adjustment mechanisms but the second players are endowed with distinct rationality levels. Based on tools of symbolic computations, we introduce a new approach and use it to establish rigorous conditions of the local stability for these models. We analytically investigate the bifurcations and prove that the period-doubling bifurcation is the only possible bifurcation that may occur for all the considered models. The most important finding of our study is regarding the influence of players' rational levels on the stability of heterogeneous duopolistic competition. It is derived that the stability region of the model where the second firm is rational is the smallest, while that of the one where the second firm is boundedly rational is the largest. This fact is counterintuitive and contrasts with relative conclusions in the existing literature. Furthermore, we also provide numerical simulations to demonstrate the emergence of complex dynamics such as periodic solutions with different orders and strange attractors.
翻译:本文旨在调查各式各样的Cournot duopoly游戏的动态, 首先玩家采用相同的梯度调整机制, 但第二玩家具有不同的理性水平。 根据象征性计算工具, 我们引入了一种新的方法, 并用它来为这些模型建立严格的当地稳定条件。 我们分析调查了两极分立, 并证明这段时期的两极分解是所有考虑过的模型唯一可能发生的两极分解。 我们研究的最重要结论是关于玩家的理性水平对多元双极竞争稳定的影响。 它的推论是, 第二家公司为理性的模型的稳定性区域最小, 而第二家公司为绝对理性的模型区域是最大的。 这一事实是反直观的, 与现有文献中的相对结论形成对比。 此外, 我们还提供数字模拟, 以证明复杂的动态的出现, 例如以不同顺序和奇怪的吸引者为周期解决方案的周期性动态的出现。