Impact of social punishment on networked evolutionary games via semi-tensor product method

This paper investigates the modeling and control of networked evolutionary games based on prisoner's dilemma game with punishment strategy. The networked evolutionary game is expressed as a logical dynamic system and then converted into its algebraic form relying on the matrix expression of logic and the method of semi - tensor product of matrices. Next, based on the algebraic form, the dynamic behavior of the networked evolutionary game is discussed. Some free-type control sequences are designed to make all players cooperate. Finally, an illustrative example is given to show the effectiveness of our main results.