This　paper　proposes　an　efficient　fast-optimal　balanced　differential　game　(DG)　approach　to　address　the　formation　control　problem　in　dynamic　environments　for　networked　multi-agent　systems　(MASs).　Compared　to　existing　receding　horizon　distributed　differential　game　(RH-DDG)　approaches,　the　proposed　approach　employs　a　two-layer　game　structure　to　balance　optimality　and　real-time　performance,　with　a　focus　on　formation　control,　collision　avoidance　and　obstacle　avoidance.　In　the　offline　layer,　the　problem　is　converted　into　a　distributed　differential　game　(DDG)　where　each　agent　computes　strategies　using　distributed　information　from　locally　neighboring　agents.　The　strategy　of　each　agent　self-enforces　a　unique　global　Nash　equilibrium　(G-NE)　with　a　strongly　connected　communication　topology,　providing　an　optimal　reference　trajectory　for　the　online　game.　In　the　online　layer,　a　receding　horizon　differential　game　with　an　event-trigger　mechanism　(RH-DGET)　is　presented　to　track　the　G-NE　trajectory.　Ego　players　are　triggered　to　update　online　Nash　strategies　only　when　the　event-triggering　condition　is　satisfied,　ensuring　the　real-time　safety　certificate.　Rigorous　proofs　demonstrate　that　the　online　Nash　strategies　converge　to　the　offline　G-NE　until　the　trigger　ends,　and　a　certain　dwell　time　condition　is　given　to　prevent　the　Zeno　behavior.　Simulation　results　validate　the　effectiveness　of　the　proposed　approach.