This article focuses on the Pareto optimal issues of nonlinear game systems with asymmetric input saturation under dynamic event-triggered mechanism (DETM). First, the safe control is guaranteed by transforming the system with safety constraints into the one without state constraints utilizing barrier function. The united cost function integrating nonquadratic utility function is constructed to provide the foundation to achieve the Pareto optimal solutions. Then, the adaptive dynamic programming method with concurrent learning is proposed to approximate the Pareto optimal strategies wherein both current and historical data are utilized. To further lessen the consumptions of computation/communication resources, the DETM is integrated into the adaptive algorithm framework which can avoid Zeno phenomena. All the signals of the closed-loop system are proved to be uniformly ultimately bounded. Finally, the simulation results are given to validate the effectiveness of the proposed method from several aspects.