Abstract:

As a retail model driven by live streaming content and brands， live e-commerce channels possess both pricing and experiential advantages， creating a competitive relationship with traditional e-commerce channels. A traditional and live-streaming dual-channel sales system is examined， comprising a brand and a streamer. The brand operates two e-commerce sales channels： the traditional channel and the live-streaming channel.

In the traditional channel， the brand enhances its brand reputation through online advertising investments. Simultaneously， the brand engages a streamer to sell products through the live-streaming channel. The popularity of live-streaming is influenced by both the brand's reputation and the streamer's effort level. Therefore， the brand considers whether to establish a live-streaming channel， modeling a differential game for both the traditional and dual-channel （traditional plus live-streaming） scenarios. Using Pontryagin Maximum Principle， equilibrium solutions for brand reputation， live-streaming popularity， and the brand's profit are derived， enabling a dynamic analysis of pricing strategies， advertising investment strategies， and live-streaming strategies.

It is revealed that brand reputation changes monotonically regardless of whether a live-streaming channel is established. After introducing the live-streaming channel， changes in live-streaming popularity are related to the initial brand reputation level. Market cannibalization exhibits two critical thresholds impacting demand in both traditional and live-streaming channels， boosting product demand in the live-streaming channel while encroaching upon market share in the traditional channel. Furthermore， upon establishing a live-streaming channel， the brand reduces product prices to alleviate competition between the traditional and live-streaming channels.

When brand reputation has a minor impact on product demand， introducing a live-streaming channel increases advertising investment and brand reputation levels. However， as brand reputation's influence grows， establishing a live-streaming channel can damage brand reputation， prompting brands to refrain from doing so. When fees are low， a lesser impact of brand reputation on product demand leads to higher advertising investment and brand reputation levels， encouraging brands to establish live-streaming channels. If slot fees are moderate， an appropriate level of brand reputation's influence on product demand and live-streaming popularity can ensure that establishing a live-streaming channel benefits the brand. Otherwise， profits from the live-streaming channel may not compensate for losses in the traditional channel， leading brands to abandon the idea of establishing a live-streaming channel. A bargaining model between traditional and live-streaming channels is established， revealing a unique negotiated market cannibalization coefficient that achieves Nash bargaining equilibrium for both channels

Key words: live e-commerce, channel strategy, brand goodwill, live-streaming popularity, differential game