Askar Sameh S, Al-Khedhairi A
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
Entropy (Basel). 2020 Feb 3;22(2):173. doi: 10.3390/e22020173.
We analyzed a dynamic duopoly game where players adopt specific preferences. These preferences are derived from Cobb-Douglas utility function with the assumption that they depend on past choices. For this paper, we investigated two possible cases for the suggested game. The first case considers only focusing on the action done by one player. This action reduces the game's map to a one-dimensional map, which is the logistic map. Using analytical and numerical simulation, the stability of fixed points of this map is studied. In the second case, we focus on the actions applied by both players. The fixed points, in this case, are calculated, and their stability is discussed. The conditions of stability are provided in terms of the game's parameters. Numerical simulation is carried out to give local and global investigations of the chaotic behavior of the game's map. In addition, we use a statistical measure, such as entropy, to get more evidences on the regularity and predictability of time series associated with this case.
我们分析了一个动态双头垄断博弈，其中参与者采用特定的偏好。这些偏好源自柯布 - 道格拉斯效用函数，并假设它们取决于过去的选择。在本文中，我们研究了该建议博弈的两种可能情况。第一种情况仅考虑关注一个参与者所采取的行动。此行动将博弈的地图简化为一维地图，即逻辑斯谛映射。通过解析和数值模拟，研究了该映射不动点的稳定性。在第二种情况中，我们关注两个参与者所采取的行动。计算了这种情况下的不动点，并讨论了它们的稳定性。根据博弈参数给出了稳定性条件。进行了数值模拟以对博弈地图的混沌行为进行局部和全局研究。此外，我们使用一种统计量度，如熵，来获取与该情况相关的时间序列的规律性和可预测性的更多证据。
