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Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization
Chaos, Solitons & Fractals ( IF 7.8 ) Pub Date : 2021-04-13 , DOI: 10.1016/j.chaos.2021.110936
Hui Li , Wei Zhou , A. A Elsadany , Tong Chu

A dynamic Cournot duopoly model with isoelastic demand function and knowledge spillover effects is established, in which the goals of two enterprises are relative profit maximization. Since these two enterprises only have incomplete information of the market, then it is assumed that the enterprises are boundedly rational, and they need to adjust their production decision in next period according to the gradient adjustment mechanism. Sufficient conditions for the existence and stable properties of unique Nash equilibrium can be judged with the help of the Jury criterion. The size of stability region is related to the values of parameters and the system has two different paths to chaos, one is via flip bifurcation and another is via Neimark-Sacker bifurcation. Finally, the complex dynamic characteristics also can be further studied by using numerical simulation, including the structures of multi-layer Arnold's tongues and coexistence of attractors.



中文翻译:

具有知识溢出效应和相对利润最大化的古诺双寡头博弈中的稳定性,多重稳定性和不稳定性

建立了具有等弹性需求函数和知识溢出效应的动态Cournot双寡头模型,其中两个企业的目标是相对利润最大化。由于这两个企业仅具有不完整的市场信息,因此假定企业是有限理性的,并且他们需要根据梯度调整机制在下一时期调整其生产决策。可以借助陪审团标准来判断唯一Nash平衡存在和稳定性质的充分条件。稳定区域的大小与参数值有关,系统有两种不同的混沌路径,一种是通过翻转分叉,另一种是通过Neimark-Sacker分叉。最后,

更新日期:2021-04-13
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