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基于双寡头企业R&D竞争模型,利用动力系统分支理论和混沌经济学原理,构建一个带有政府研发补贴的有限理性双寡头企业动态博弈模型,分析离散动态系统中政府研发补贴系数对R&D竞争均衡条件的限制作用及对整个双寡头市场运作状态的动态影响,并进行数值仿真。研究表明:1)Nash均衡条件下,合理的补贴系数取值范围应受到市场需求函数、有限理性企业R&D投入调速以及产品成本的约束。适当的补贴率有助于系统维稳,而不适当的补贴率则会使得R&D竞争进入混沌状态。2)补贴政策实行初期,市场会呈现出短暂的不均衡状态。双寡头企业前期R&D投入波动幅度大于利润波动幅度,且两者皆与补贴力度正相关。3)双寡头市场中,政府R&D补贴能够刺激企业加大R&D投入,并使得R&D投入调速较快的企业将取得更高的利润,而调速较慢的企业则会处于相对劣势。文章最后通过讨论给出政策层面上的相关建议,以期为相关研发补贴政策的制定提供参考。
Based on the R & D competition model of duopoly enterprises, a dynamical game model of bounded duopoly firms with government R & D subsidies is constructed by using the theory of dynamic system bifurcation and chaos economics. The dynamic R & D competition equilibrium of R & D competition in discrete dynamic systems is analyzed The restrictive role and the dynamic impact on the operation of the entire duopoly market, and numerical simulation. The research shows that: 1) Under the condition of Nash equilibrium, the reasonable range of subsidy coefficient should be constrained by the market demand function, the R & D input speed regulation and the product cost of the bounded rational enterprise. The appropriate subsidy rate helps to maintain the stability of the system, but the inappropriate subsidy rate will make R & D competition into chaos. 2) In the early days of the subsidy policy, the market will show a transient imbalance. The volatility of R & D investment of duopoly enterprises in the early period is greater than the fluctuation of profits, and both of them are positively correlated with the subsidies. 3) In the duopoly market, government R & D subsidies can stimulate enterprises to increase R & D investment, and make R & D investment faster enterprises will achieve higher profits, while slower speed enterprises will be at a relative disadvantage. Finally, the article gives some suggestions on the policy level through discussions, in order to provide reference for the development of subsidy policy for R & D.