Should live-streaming platforms nonexclusively promote brands from traditional retail platforms?

In a live-streaming channel, brands' products are sold to consumers through promotions by live-streaming platforms. Specifically, the live-streaming platform can not only exclusively promote products for brands on its own platform but also nonexclusively promote products for brands from traditional retail platforms (traditional platforms). In this paper, we distinguish the influence of consumer behavioral characteristics on demand between live-streaming and traditional platforms. By developing two game models, we investigate whether the live-streaming platform should promote products for brands nonexclusively. Counterintuitively, when the live-streaming platform adopts exclusive promotion, a higher live-streaming platform's commission rate may be beneficial to the brand on it. Equally surprisingly, with nonexclusive promotion strategy, the traditional platform benefits more with the live-streaming platform's promotional ability under certain conditions. If the promotion cost coefficient is sufficiently high, the live-streaming platform should choose the exclusive promotion strategy; otherwise, it may adopt the nonexclusive promotion strategy. We further obtain the conditions for live-streaming platforms and brands from traditional platforms to cooperate. That is, given the impacts of the promotion cost coefficient and live-streaming platform's commission rate, the solo win-win situation is the exclusive promotion strategy, while given the impacts of the promotion cost coefficient and promotion fee, a win-win situation occurs under both the exclusive and nonexclusive promotion strategies.