Evolutionary Game And Control In Enterprise Innovation Networks

Enterprises are the important force that combines science and technology and economy closely.As the main body of technology innovated decision-making,research and development investment,scientific research organization and achievement transformation,enterprise innovation is the only way for development.Therefore,it is extremely significant to research the mechanism of enterprise innovation.Using the semi-tensor product of matrices,we study the evolutionary game and the optimal control of enterprise's innovation network.According to the position of the enterprise,a multi-layer network evolution game model is established,and through the analysis of its structure matrix,the entire enterprise innovation networked evolutionary trend is achieved.Based on the analysis of dynamic games,by controlling a part of enterprises' strategy,the desired goals that all enterprises innovation is achieved.The main results are as follows:(1)Using the semi-tensor product method,the dynamics of the multi-layer evolutionary networked game is converted to the algebraic formulation for the game.Based on the structure matric,the dynamic behavior of the multi-layer evolutionary networked games is discussed.The strategy optimization problem is considered by adding a pseudo-player.The aim is to maximize the average income of pseudo-players by designing optimal controlling sequence.An illustrative example shows the effectiveness of these results.(2)With “Boxed pigs game” as the normal game,the process of evolutionary game for enterprise innovation network is studied by using the semi-tensor product method.Considering the enterprise profit function,the necessary and sufficient condition for the game optimal and stable Nash equilibrium point is obtained.To achieve all the enterprise innovation,which is Nash equilibrium.We consider implement of government regulation by using reward and punishment for enterprises that they take different strategies.(3)The evolutionary game and control optimization of the enterprise innovation network is studied.Firstly,the multi-layer coupled evolutionary game model is set up,enterprises of the same scale have the same properties.Then based on the finite normal game theory,we get the strategy of enterprises at each moment by using the semi-tensor product method and the cascading myopic best response adjustment.Furthermore,a pinning control algorithm is designed to reach the objective that all enterprises choose innovation strategy,which is a stable profile.An illustrative example is given support our results.