The Analysis And Control Of Networked Evolutionary Boxed Pig Games Based On The Mechanism Of Reward And Punishment

By using the semi-tensor product method,this paper investigates the analysis and control of networked evolutionary boxed pig games based on the mechanism of passive and active reward and punishment.The main contents of this paper are listed as follows:1.The algebraization and optimization of networked evolutionary boxed pig games with the mechanism of passive reward and punishment is studied.An algorithm is provided to construct the algebraic formulation for the dynamics of the passive reward and punishment networked evolutionary boxed pig games,and a necessary and sufficient condition is presented to detect whether the dynamic process of the game starting from any initial profile except full defection can converge to full cooperation state.By discussing the impact of reward and punishment parameters on the final cooperation level of the whole network,the optimization problem is considered,and the value of reward and punishment is obtained to maximize the number of elements in the convergence domain of the game.2.The dynamic process of control networked evolutionary boxed pig games with the mechanism of active reward and punishment is studied.The corresponding control sequences are designed and a necessary and sufficient condition which can make the whole evolutionary process converges to the state of completely cooperation is obtained,the option method of the initial states is given to make the evolutionary dynamics reach to the state of completely cooperation under a sequence of controls,the impact of parameters on the final cooperation level are discussed simply.