具有不同决策规则的Cournot双寡头模型分析

ANALYSIS OF COURNOT DUOPOLY MODEL WITH DIFFERENT DECISION RULES

以寡头市场中两家具有有限理性且以产量竞争的异质企业为背景,建立了一个离散时间的非线性动态古诺双寡头模型.讨论了模型的边界均衡点和Cournot-Nash均衡点的存在性和稳定性,给出了CournotNash均衡点的稳定区域.通过数值模拟,利用单参数分岔图分析了随着参数的变化,系统的复杂动力学行为的变化情况.得出调整速度太大会导致Cournot-Nash均衡点失去稳定性,系统将产生混沌吸引子等复杂的动力学现象.此外初值极小的变化将导致系统产生巨大的波动.同时企业成本函数的差异性也会使得系统产生不同的分岔.

This paper is based on the quantity competition for two heterogeneous and bounded rational firms in the oligopoly market. A nonlinear dynamic Cournot duopoly model is constructed in discrete time, and the existence and stability of the boundary equilibrium point and the Cournot-Nash equilibrium are analyzed. The stability region of the Cournot-Nash equilibrium is given. Numerical simulation and bifurcation diagrams are used to study the complex dynamic behaviour of the system with the varying parameters chosen in the parameter space. It is conclude that the Cournot Nash equilibrium loses its stability, and the chaotic attractor or other complex dynamic behaviours arise when the speed of adjustment is too high. Furthermore,a tiny variation of the initial conditions causes the drastic fluctuations in the output. The heterogeneous cost function of the system also gives rise to different bifurcation at the same time.