How cooperation arises from rational players?  

作　　者：MU YiFen GUO Lei 

机构地区：[1]Institute of Systems Science, Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Science China(Information Sciences)》2013年第11期243-251,共9页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.60821091)

摘　　要：In classical control systems, the plant to be controlled does not have intention to gain its payoff or benefit, which is obviously not the case in various aspects of social and economic systems（or subsystems）. In the latter case, competition and cooperation between players who will optimize their own payoffs turn out to be an important feature, and a fundamental problem is how to achieve cooperation from these rational players. In this paper, we present a neat way to lead to cooperation in dynamical Prisoner＇s Dilemma game. In our scenario, the two players are heterogenous with hierarchical roles as the ＇leader＇ and the ＇follower＇ respectively. It is shown that the system will co-evolve into and stay at the cooperation state if and only if the leader is restricted not to take the dominating strategies. For the special case of 1-step-memory, the optimal strategies for the leader and follower are ＇Tit for Tat＇ and ＇ALL C＇ respectively. In this framework, both the heterogeneity of the players＇ roles and the multiplicity of time-scales are crucial for cooperation, which are quite natural settings from the view point of control theory. Besides, the boundary for cooperation also turns out to depend on the relative payoffs of the players.In classical control systems, the plant to be controlled does not have intention to gain its payoff or benefit, which is obviously not the case in various aspects of social and economic systems（or subsystems）. In the latter case, competition and cooperation between players who will optimize their own payoffs turn out to be an important feature, and a fundamental problem is how to achieve cooperation from these rational players. In this paper, we present a neat way to lead to cooperation in dynamical Prisoner＇s Dilemma game. In our scenario, the two players are heterogenous with hierarchical roles as the ＇leader＇ and the ＇follower＇ respectively. It is shown that the system will co-evolve into and stay at the cooperation state if and only if the leader is restricted not to take the dominating strategies. For the special case of 1-step-memory, the optimal strategies for the leader and follower are ＇Tit for Tat＇ and ＇ALL C＇ respectively. In this framework, both the heterogeneity of the players＇ roles and the multiplicity of time-scales are crucial for cooperation, which are quite natural settings from the view point of control theory. Besides, the boundary for cooperation also turns out to depend on the relative payoffs of the players.

关 键 词：COOPERATION Prisoner＇s Dilemma leader-follower game finite-memory strategy OPTIMIZATION 

分 类 号：O231[理学—运筹学与控制论]