基于半张量积的企业创新网络演化博弈

Evolutionary enterprise innovation networked game based on the semi-tensor product of matrices

当代经济环境下,创新已经成为企业生存发展的必要条件。将所有企业按规模分为大小两种企业,建立企业创新双层耦合网络,并研究了企业间的博弈过程。首先,运用矩阵半张量积方法,以"智猪博弈"为基本博弈,得到每一时刻各企业的策略,而非企业总体创新的比例;其次,根据收益函数得到整个企业创新网络的最优稳定纳什均衡点;最后,增加政府调控,改变博弈基本支付矩阵,从而达到最优稳定纳什均衡状态,即所有企业全部创新。

In the contemporary economic environment,innovation has become the inevitable condition for the survival and development of enterprises.In this paper,all the enterprises were classified into two categories according to the scale,establishing a double-layer coupling network of enterprise innovation,and the process of the game between enterprises was studied.Firstly,taking“Boxed Pig Game”as the basic game,the semi-tensor product method was used to get the strategy of each enterprise at every moment,not the proportion of the enterprise overall innovation.Secondly,the optimal stability for the Nash equilibrium of the whole enterprise innovation network was reached according to the payoff function.Finally,the government regulation was introduced to change the basic matrix of the game and therefore reach a stable state of the optimal Nash equilibrium;that is,all enterprises realized innovation all round.