具有二次成本函数的双寡头博弈模型分析

Analysis of Duopoly Game Model with Quadratic Cost Function

基于有限理性预期与适应性预期对企业的生产产量进行调整,构建了具有二次成本函数的双寡头市场的产量博弈模型。采用二次成本函数和GD调节机制,通过长期博弈进行产量调整以实现最优利润。研究了具有二次成本函数的双寡头博弈模型的动力学演化性质。讨论了企业的调整速度波动以及企业的产品差异化系数对模型稳定性的影响。理论分析和数值仿真均表明,采取有限理性预期企业的调整速度以及两家企业的产品差异化系数很大程度上会对博弈结果产生影响,这也为企业在市场中的产量决策提供了理论基础。

Based on the bounded rational expectation and adaptive expectation,the output game model of duopoly market with quadratic cost function is constructed.The quadratic cost function and GD regulation mechanism are used to adjust the output through long-term game to achieve the optimal profit.The dynamic evolution properties of the duopoly game model with quadratic cost function are studied.The influence of yield adjustment rate fluctuation on model stability is discussed.Both theoretical analysis and numerical simulation show that the degree of substitution between products,the investment adjustment rate of players will have a great impact on the game results.This also provides a theoretical basis for the players’production decisions in the market.