Modeling and Dynamics of Networked Evolutionary Game With Switched Time Delay

Time delay is inevitable in information communication. Switched time delay, as a time-varying delay, plays an important role in information interaction between agents. In this article, networked evolutionary games (NEGs) with switched time delay are investigated, including modeling and dynamics analysis. First, the dynamic model of the delayed NEG is proposed, then the algebraic formulation is established by using the algebraic state-space approach. Second, dynamic behavior of the game is discussed, involving general convergence and evolutionarily stable profile analysis. Necessary and sufficient conditions are derived for convergence of the game and evolutionarily stable profile, respectively. Finally, two illustrative examples are employed to demonstrate the validity of the theoretical results.