Appendix.

<div><p>Investigating novel collaboration modes is imperative for enhancing the cooperative ties between brand retailers and anchors as live streaming commerce moves progressively towards standardization. In this paper, we study a live streaming commerce supply chain system composed of a brand retailer and an Internet celebrity anchor. We also develop the pricing and live streaming service effort decision models under the equal proportion settlement mode of pit fee for the brand retailer and anchor. The research results show that under certain conditions, there is an optimal joint decision on price discount and live streaming service effort. In addition, the equal proportion settlement mode provides security for brand retailers but tends to expose the anchor’s capabilities of live streaming sales. Consequently, anchors can only obtain a higher proportion of the pit fee by putting in more effort. Finally, through numerical analysis, we presented the impact of key parameters on the optimal decisions, demand, and profits of brand retailers and anchors. Based on these findings, we provided relevant managerial insights, offering valuable guidance and reference for the live streaming commerce industry.</p></div>