Notations and descriptions.

This study examines the pricing policies and the dual-channel strategies in a two-tier supply chain where a manufacturer distributes products through a retailer and considers the opening of a traditional direct online channel or a live-streaming sales channel The manufacturer has three sales modes, i.e., traditional retail channel only, opening a traditional direct online channel and opening a live-streaming direct sales channel, to consider. The manufacturer and the retailer play a Stackelberg game wherein the manufacturer has the first mover advantage. The two supply chain members can follow two decision sequences where the manufacturer decides the direct online retail price before the retailer does in one, and the manufacturer and the retailer cooperate to decide the retail prices simultaneously in the other. The profit optimization models for the three sales modes are formulated, and the closed forms of the optimal solutions are then derived through backward induction. The optimal pricing decisions and profits with different decision sequences are compared and analyzed among the three sales modes. The results suggest that the manufacturer should introduce a live-streaming direct sales channel when facing fierce competition, and should not introduce a dual channel to create a win-win situation for the two supply chain members when facing mild competition. The manufacturer should increase the wholesale and the direct online retail prices and make more live-streaming sales effort, and the retailer should also increase the retail price, if the streamer has good sales skills when introducing a live-streaming sales channel. The manufacturer and the retailer should decide the retail prices simultaneously when a live-streaming sale channel is introduced.