When should suppliers introduce a live-stream channel: The role of limited supply capacity

The growth of e-commerce has driven numerous suppliers to adopt live-stream channels. However, most studies fail to account for capacity limitations in supply chains. This study examines a supplier with limited capacity collaborating with a streamer to conduct live-stream sales. Using a game-theoretical approach, we analyze how capacity constraints affect a supplier's decision to introduce live streaming through either direct or reselling channels. Our analysis reveals that a supplier is more likely to adopt a live-stream channel when the commission rate and consumers’ additional costs associated with the live-stream channel are relatively low, provided capacity is not severely limited. Interestingly, even with a reselling channel, a supplier may benefit from a live-stream channel when consumer costs are relatively high. Moreover, a supplier with moderate capacity can sustain a live-stream channel at higher consumer costs than a supplier with low capacity. The study also reveals that the introduction of a live-stream channel always increases consumer surplus but does not consistently improve social welfare unless capacity is relatively abundant. Suppliers using direct channels require greater capacity to enhance social welfare than those using reselling channels. Furthermore, these results are robust across various extensions of the model.