Modeling and optimization control of networked evolutionary games with heterogeneous memories and switched topologies

摘要

In evolutionary games, the shared information and topologies between different players mostly may be inequable and changeable dynamically, which bring many challenges for analysis and optimization control of networked evolutionary games (NEGs). Therefore, this paper investigates an optimization control problem of NEGs with heterogeneous memories and switched topologies. Firstly, the NEG with heterogeneous memories and switched topologies is modeled as a logical system, and its algebraic form is proposed by using the semi-tensor product (STP) of matrices. Secondly, to guarantee the convergence of the optimal augmented strategy profile from the initial one, we judge the existence of control sequences, which can satisfy that all players’ payoffs exceed the threshold. Furthermore, the method to design the control sequences is given, which is followed by a verification for the rationality of the control sequences. Finally, a typical example is given to demonstrate the above theoretical results.