<p>Brand self-live streaming and influential streamer live streaming are two typical cooperation modes in the live streaming e-commerce supply chain. When an incumbent brand dominates the market, a competitive brand merchant that seeks to enter new markets through a live streaming e-commerce platform must carefully choose its cooperation mode. To address this challenge, this study develops a three-party Stackelberg game model involving a competitive brand merchant, an incumbent brand merchant, and a platform with an advantage in demand information. The model examines how information sharing and traffic investment affect cooperation mode selection. The results show that: (1) Traffic cost and commission rate are the core constraints of cooperation mode choice. Influential streamer live streaming dominates under low traffic cost, while brand self-live streaming provides stronger control under high commission rates. (2) Platform information sharing exhibits mode dependence. Under brand self-live streaming, the platform has a persistent incentive to share demand information. (3) Supply chain members achieve win–win outcomes under different conditions. At low (high) traffic cost, influential streamer live streaming (brand self-live streaming) is superior. (4) Overall supply chain efficiency varies across contexts. At moderate traffic cost, brand self-live streaming performs better, whereas low traffic cost with an appropriate commission rate favors influential streamer live streaming.</p>