Analysis,Control And Application Of Networked Evolutionary Games-the Semi-Tensor Product Method

As an effective tool for the study of logical dynamic networks,the semi-tensor product of matrices not only develops a new research direction for the study of networked evolutionary game,but also promotes the research on the micro-aspects of evolution game in social and economic systems.If enterprises are regarded as points in the network and the relationships between enterprises are represented as edge,the social network of enterprises will be formed.Then the networked evolutionary game is formed when the evolutionary game between enterprises is repeated.In this paper,the algebraic expression of a class of pinning control networked evolutionary game and two kinds of enterprises innovation networked evolutionary game are obtained by semi-tensor product,and different control ways are designed to control the evolution of game to the best strategy profile.The main results are as follows.(1)Firstly,the problem of algebraic formulation and strategy optimization of networked evolutionary game with pinning control is studied.Game evolution follows the myopic best response adjustment rule.The basic evolution equation of each player and the overall profile evolution equation of the network are obtained via the semitensor product.A free-type pinning control sequence is designed to guarantee the desired strategy profile reachable globally with the reverse-transfer method.(2)Secondly,the theory of networked evolutionary game is applied to study the enterprise innovation networked evolutionary game.Considering that the network structure will change with the change of the relationship between enterprises in practice and the enterprise may update the strategy according to the information of multiple historical moments,the model of the evolutionary game with time delays of enterprise cooperative innovation under switching topology is established.The revenue of the game,the evolution of the strategic profile and the switching of game networks are formulated separately via the semi-tensor product.The algebraic expression of the process of evolutionary game enterprise innovation under switching topology is obtained.The control input is designed and the necessary and sufficient conditions for all enterprises to participate in cooperative innovation are obtained.(3)Finally,the evolutionary game of probabilistic asymmetric enterprise cooperative innovation network is studied.A two-layer coupled network model reflecting asymmetric enterprise cooperative innovation is established.The strategy is updated by probabilistic unconditional imitation.The algebraic expression of the game is obtained via the semi-tensor product,and the behavior of games is analyzed based on the algebraic form.The necessary and sufficient conditions for all enterprises to participate in cooperative innovation with probability 1 is given.By changing the proportion of excess return distribution and default cost,designing the control algorithm to ensure that all enterprises choose the strategy of cooperative innovation with probability 1.