相对利润最大化下二次成本的量子古诺模型的动力学

Dynamic Anaysis of a Quantum Cournot Model Based on Relative Profit Maximization

摘要: 采用梯度调节机制建立了一个基于相对利润最大化下的量子古诺模型，并利用雅可比矩阵以及jury判据对唯一Nash均衡点的局部稳定性进行了分析。并通过数值模拟对系统的局部分岔行为以及参数影响进行了分析。结果表明，当调整速率过大时，系统会处于不稳定的状态。此外，更大的量子纠缠将降低系统对初始条件的敏感依赖性。

Abstract: A quantum Cournot model based on relative profit maximization is established by using the gradi-ent adjustment mechanism. The Jacobian matrix and Jury’s criterion were used to analyze the local stability of the unique Nash equilibrium point. The local bifurcation behavior and parameter influ-ence of the system were analyzed by numerical simulation. The results show that when the adjust-ment rate is too large, the system is in an unstable state. In addition, larger quantum entanglement will reduce the sensitivity dependence of the system on initial conditions.