Optimal Power Structure and Operational Incentives in Live-Streaming Commerce: A Game-Theoretic Analysis of Streamer Influence

The rapid evolution of live-streaming commerce has reshaped retail supply chains, shifting market dominance from manufacturers to influential streamers. Despite this shift, the internal mechanisms selling efforts and paid traffic acquisition—remain underexplored. To bridge this theoretical gap, we develop a game-theoretic framework to model the endogenous power structure, comparing the Streamer-led Top-tier (KS) mode and the Brand-led Ordinary (MS) mode. Our analytical results reveal three key theoretical insights. First and foremost, we identify a strict positive monotonicity between streamer influence and equilibrium decisions. Regardless of the power structure, an increase in influence consistently drives the streamer to intensify operational inputs, while simultaneously inducing the brand to raise the direct selling price. In the second place, consumer sensitivity acts as a positive driver for the Top-tier mode. Higher sensitivity motivates the streamer to scale up selling efforts and paid traffic volume, which corresponds with an optimal increase in the brand's retail price. Moreover, the Top-tier mode exhibits negative sensitivity to operational costs. We prove that rising costs force a significant reduction in the streamer's operational portfolio and a subsequent decrease in the brand's price, indicating that the high-input equilibrium is constrained by cost frictions. From a managerial perspective, numerical experiments reveal a "Consensus on Scale" but a "Conflict on Structure." Specifically, brands maximize profit by collaborating with top-tier streamers, while streamers maximize profit by attaining top-tier influence. However, regarding mode selection, the brand secures significantly higher profitability in the KS mode than in the MS mode, even though the streamer holds channel leadership. Conversely, the streamer generates lower profits in the KS mode than in the MS mode, revealing a "Leadership Trap" where heavy operational burdens outweigh the strategic benefits of dominance.