The central focus of our investigation revolved around the convergence of agents' behavior toward a particular invariant distribution and determining the characteristics of the optimal strategies' distribution within the framework of a dynamical Multi-Local-Worlds complex adaptive system. This system was characterized by the co-evolution of agent behavior and local topological configuration. The study established a representation of an agent's behavior and local graphic topology configuration to elucidate the interaction dynamics within this dynamical context. As an illustrative example, we introduced three distinct agent types—smart agent, normal agent, and stupid agent—each associated with specific behaviors. The findings underscored that an agent's decision-making process was influenced by the evolution of random complex networks driven by preferential attachment, coupled with a volatility mechanism linked to its payment—a dynamic that propels the evolution of the complex adaptive system. Through simulation, we drew a conclusive observation that even when considering irrational behaviors characterized by limited information and memory constraints, the system's state converges to a specific attractor. This underscored the robustness and convergence properties inherent in the dynamical Multi-Local-Worlds complex adaptive system under scrutiny.