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.