寡头垄断市场下量本利复杂性分析

Complexity analysis about cost, sales volume and profit in duopoly

以动态古诺模型为基础,在需求函数是非线性、成本函数是线性的情况下分析了企业的量本利动态演化的博弈模型,对离散动态系统的Nash均衡的稳定性进行了分析.当模型的某些参数在一定范围内变化时,Nash均衡点失去稳定性,经倍周期分叉后出现混沌态.结果表明,参与人对产量的调整速度越小或单位变动成本越大,其利润就越稳定.同时用数值方法模拟了2个参数同时变化时系统复杂的动态性.从2个参数同时变化时的等周期图和混沌图,可观察到导致周期态、混沌态的不同路径.

According to a dynamic Cournot model, the dynamical game model on cost, sales volume and profits of corporations is analyzed under the conditions that demand function is non-linear and the cost function is linear. The stability of the equilibrium of the discrete dynamical system is studied. As some parameters of the model vary, the stability of Nash equilibrium would lose and the complex chaotic behavior occurs. Numerical results show that the player's profits become more stable if the speed of adjustment decreases or variable cost per unit increases. Using reliable numerical methods, the complex dynamical behavior of the model are studied when two parameters are simultaneously varied. Several different routes to chaos can be found in iso-period plot and chaos plot.