In this paper, a Cournot model and its dual Bertrand model where firms have comprehensive preferences are developed. The preference was proposed by Bowles (2004) based on the results of Rabin (1993) and Lebine (1998). Comparable static method is used to illustrate the impact of parameters on equilibrium. Three scenarios are classified by preference parameter: completely cooperative, hostile to each other and general Cournot or Bertrand model. In each situation, Cournot model and its dual model present different chaos phenomenon which have various and abundant strange attractors, while the shapes of the stability regions are similar in the same situation. In the static setting, the local stability analysis of equilibrium gives the bounded region of quantity or price. The one-dimensional Logistic mapping is applied to studying the dynamics of the models on invariant axes. The critical curves classify different regions according to the number of preimages (q₁, q₂) or (p₁, p₂). Besides, simulations give more intuitive results: the cycle attractor, chaotic attractor and the basin of attraction with “holes” are presented. The article also provides new findings that under the assumption of comprehensive preference, the Cournot model with substitutes (complements) and the Bertrand model with complements (substitutes) are still duality models in the dynamic settings.

在本文中，开发了公司具有综合偏好的Cournot模型及其对偶Bertrand模型。Bowles（2004）根据Rabin（1993）和Lebine（1998）的结果提出了偏好。可比静态方法用于说明参数对平衡的影响。三种情况按偏好参数分类：完全合作，彼此敌对以及通用Cournot或Bertrand模型。在每种情况下，古诺模型及其对偶模型都呈现出不同的混沌现象，这些混沌现象具有丰富多样的奇异吸引子，而在相同情况下，稳定区域的形状相似。在静态环境中，对均衡的局部稳定性分析给出了数量或价格的有界区域。一维Logistic映射用于研究不变轴上模型的动力学。临界曲线根据原像的数量对不同区域进行分类（q ₁，q ₂）或（p ₁，p ₂）。此外，模拟给出了更直观的结果：呈现了循环吸引子，混沌吸引子和带有“孔”的吸引盆。本文还提供了新的发现，即在假设综合偏好的情况下，具有替代品（补体）的古诺模型和具有补体（替代品）的Bertrand模型在动态环境下仍是对偶模型。