Strategy synchronization of multi-player systems

Consider a controlled networked evolutionary game(NEG), where the agents consist of controlled ones and control ones. The controlled agents follow a simple rule, called the strategy updating rule, and the strategies of control agents need to be designed. The problem of synchronization is considered. First, an NEG is formulated as a dynamic system via algebraic state space representation (ASSR). Then two approached are proposed: (i)When the controls are allowed to use global information, the necessary and sufficient conditions are revealed. (ii) The aggregation of NEGs is proposed. The dynamics of each aggregated block of a partition is converted into a switched logical dynamic system. Then certain stabilization results for switched logical dynamic systems are obtained. Using the stabilization results to each blocks, a sufficient condition is obtained for the synchronization of overall NEGs. The second approach is suitable for large-scale NEGs.