The Using Of Semi-tensor Product Of Matrices In The Network Evolutionary Games And Logic Operator In Tensor

Using the framework of semi-tensor product of matrices the evolutionary stability strategy in evolutionary game theory is studied.In addition,using the rule of tensor and matrix multiplication,the matrix representation of a logical operator is transformed into a tensor representation of a logical operator.At the same time,we discussed the mechanism of the variation of join in the network game in the snowdrift game evolution model and its dynamic evolution process is also studied.Then,the network evolutionary game model and control problem of prisoner's dilemma game based on social penalty is discussed,and the dynamic behavior is discussed by adding control sequence.This paper's main contributions are:(1)Problems of the evolutionary stable strategy in evolutionary games are discussed,and provide a new method of evolutionary stable strategy in the basic analysis model of evolutionary game under bounded rationality by using the properties of Pseudo Boolean functions.(2)The tensor representation of logical operators is studied.Under the rule of multiplication of tensor and matrix,the tensor expression of the corresponding logic operator is obtained by using the truth table of the logical operator.(3)The evolutionary model of variation mechanism of the snowdrift game added return network was set up,combined with the logic of the dynamic system,then turned into algebra,and discussed the final cooperation stability.(4)The evolutionary network game with punishment strategy is studied and the algebraic form of the evolutionary dynamic of the game is obtained.A necessary and sufficient condition is given to design a free-type control sequence to make all players cooperate.