Summary: In this article, a new event-based adaptive critic algorithm with multiple triggering conditions is investigated to address multi-player nonzero-sum game problems for discrete-time nonlinear dynamics. In order to improve resource utilization while ensure mutual independence among players, the corresponding novel triggering conditions are designed for each player. The corresponding control input is updated only when the relevant triggering condition is violated. It is emphasized that these triggering conditions are established based on the iteration of the time-triggered mechanism. Then, according to the setting triggering conditions, we prove that the real cost function possesses a predetermined upper bound, which realizes the cost guarantee of the controlled system. Additionally, the multi-player closed-loop system is proved to be asymptotically stable and the multi-event-triggered control method is implemented by constructing three kinds of neural networks. Finally, the effectiveness of the developed multi-event-triggered control approach is verified through conducting two simulation examples.
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