Population Games on Dynamic Community Networks

In this letter, we deal with evolutionary game-theoretic learning processes for population games on networks dynamically evolving communities. Specifically, propose a novel mathematical framework in which deterministic, continuous-time replicator equation community network is coupled closed dynamic flow process between communities, turn governed by an environmental feedback mechanism. When such mechanism independent of the process, closed-loop system differential equations obtained. Through direct analysis system, study its asymptotic behavior. prove that, if converges, it converges to (possibly restricted) Nash equilibrium game, even when does not converge. Moreover, class games-two-strategy matrix games-a Lyapunov argument employed establish folk theorem that guarantees convergence subset equilibria, is, stable states game. Numerical simulations are provided illustrate and corroborate our findings.