This　paper　gives　a　novel　differential　game　scheme　to　solve　the　collision　avoidance　problem　for　multi-agent　systems.　Based　on　the　concept　of　artificial　potential　field　(APF),　we　combine　obstacle　avoidance　objectives　with　trajectory　optimization　targets　as　the　performance　index.　The　feedback　strategies　are　based　on　the　solutions　of　coupled　Riccati　equations.　Furthermore,　it　is　proved　that　the　feedback　strategies　will　converge　to　a　Nash　equilibrium　(NE).　Finally,　simulation　results　are　provided　to　show　the　advantages,　which　make　agents　arrive　at　the　targeted　position　collision-free　with　a　reduced　time.　©　2022　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.