Traditional game models struggle to capture the dynamic agent-interactions over time. Leveraging multi-agent synergies, we construct a framework for dynamic evolution, underscoring the pivotal role of information distribution in shaping game outcomes. Players infer the behaviors of non-adjacent agents from the actions of their neighbors, distilling information from partial datasets. By formulating a tailored cost function and an optimal strategy, we assess the validity of this framework through Nash equilibrium solutions and Lyapunov stability criteria. Incorporating an event-triggered mechanism, we further implement the prescribed-time practical bipartite consensus. Dynamic triggering conditions inherently prevent Zeno behavior. Finally, numerical simulations confirm the theoretical results.