In this paper, we investigate two heterogeneous triopoly games where the demand function of the market is isoelastic. The local stability and the bifurcation of these games are systematically analyzed using the symbolic approach proposed by the author. The novelty of the present work is twofold. On one hand, the results of this paper are analytical, which are different from the existing results in the literature based on observations through numerical simulations. In particular, we rigorously prove the existence of double routes to chaos through the period-doubling bifurcation and through the Neimark-Sacker bifurcation. On the other hand, for the special case of the involved firms having identical marginal costs, we acquire the necessary and sufficient conditions of the local stability for both models. By further analyzing these conditions, it seems that that the presence of the local monopolistic approximation (LMA) mechanism might have a stabilizing effect for heterogeneous triopoly games with the isoelastic demand.

翻译：在本文中,我们调查了两种不同的三角游戏,其中市场的需求功能是无弹性的。当地稳定和这些游戏的两极分化使用作者建议的象征性方法进行系统分析。目前工作的新颖性是双重的。一方面,本文的结果是分析性的,与通过数字模拟观察的文献现有结果不同。特别是,我们严格证明存在通过这段时期的双倍分解和通过Neimark-Sacker两极分化而走向混乱的双轨道。另一方面,对于所涉公司具有相同边际成本的特殊情形,我们获得了两种模型当地稳定的必要和充分条件。通过进一步分析这些条件,似乎当地垄断近似机制的存在可能会对具有无弹性需求的多种三角游戏产生稳定效应。