Analysis And Control Of Networked Evolutionary Game Based On Heterogeneous Social Groups

Network science provides a systematic and effective theoretical framework for describing the relationship between players in the evolution of game.Network evolutionary game is a theory formed by the combination of complex network and evolutionary game.Through network evolutionary game,we can study the influence of game relationship on the evolution of individual behavior in a group.Birds of a feather flock together and people flock together.The differences among individuals promote the formation of heterogeneous social groups,which can be described by multi-layer coupling networks.Based on the basic theory of complex network correlation,this chapter studies and analyzes the evolutionary game dynamics among heterogeneous social groups.The main work is as follows:(1)We study the dynamics of network evolutionary games for a class of coupled social groups,in which players learn from neighbors of the same group and play with neighbors of different groups on a two-layer network model.Firstly,the payoff equation of the game is transformed into an algebraic form by using the semi-tensor product method.Based on this,the sufficient and necessary conditions for the existence of the pure strategy Nash equilibrium of the game are obtained.Secondly,according to the best response adjustment rule with group intelligence,the state transition equation of game dynamics is constructed,and the sufficient and necessary conditions for realizing group strategy consensus are obtained.(2)We study the network evolution game dynamics of a class of heterogeneous social groups.The relationship between two heterogeneous groups is described by a two-layer network model.Participants’ doubts about group wisdom and their evaluation of their current earnings are defined as participants’ social satisfaction and payment satisfaction.These two kinds of satisfaction will affect the player’s choice of strategy.Firstly,the dynamic algebraic equation of the game is obtained by using the semi-tensor product method.Secondly,the state feedback control is designed for the network evolutionary game under the influence of time delay,and the sufficient and necessary conditions for realizing group strategy consensus are obtained.(3)We study the evolution dynamics of coordinated game with pareto optimality on a twolayer WS small-world network.Different from the traditional coordination game,in this evolutionary game model,the risk value when players choose cooperation is not fixed,but is related to the strategic choice of the players in the game neighbors,and the range of risk increase or decrease is controlled by cumulative factors.The influence of the size of the accumulation factor and the size of the internal degree of the network layer on the evolution of the coordination game is discussed by Monte Carlo simulation method.